{"id":6533,"date":"2015-04-08T13:27:10","date_gmt":"2015-04-08T05:27:10","guid":{"rendered":"http:\/\/www.vbtutor.net\/?page_id=6533"},"modified":"2018-06-22T18:11:42","modified_gmt":"2018-06-22T10:11:42","slug":"visual-basic-2015-lesson-19-trigonometric-functions","status":"publish","type":"page","link":"https:\/\/www.vbtutor.net\/index.php\/visual-basic-2015-lesson-19-trigonometric-functions\/","title":{"rendered":"Visual Basic 2015 Lesson 19: Trigonometric Functions"},"content":{"rendered":"<h4 style=\"text-align: center;\"><strong><a title=\"visual basic 2015 tutorial lesson 18\" href=\"http:\/\/www.vbtutor.net\/index.php\/visual-basic-2015-lesson-18-working-math-functions\/\">[Lesson 18]<\/a>&lt;&lt;<a title=\"visual basic 2015 tutorial\" href=\"http:\/\/www.vbtutor.net\/index.php\/visual-basic-2015-tutorial\/\">[Contents]<\/a>&gt;&gt;<a href=\"http:\/\/www.vbtutor.net\/index.php\/visual-basic-2015-lesson-20-format-functions\/\">[Lesson 20]<\/a><\/strong><\/h4>\n<p>In the previous lesson, we have learned how to write code using various mathematical functions in Visual Basic 2015. In this lesson, we shall proceed to learn how to work with a group of mathematical functions that deal with angles and lengths of a triangle, they are the trigonometric functions. The three basic trigonometric functions are <strong>Sin, Cos<\/strong>, and <strong>Tan<\/strong> which stand for sine, cosine and tangent. We also deal with the inverse trigonometric functions <strong>Asin, Acos<\/strong>, and <strong>Atan<\/strong> respectively.<\/p>\n<p><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script><br \/>\n<ins class=\"adsbygoogle\" style=\"display: block; text-align: center;\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\" data-ad-client=\"ca-pub-3033628290023372\" data-ad-slot=\"4768455349\"><\/ins><br \/>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/p>\n<h2><strong>19.1 The Sin function<\/strong><\/h2>\n<p>The Sin function returns the sine value of an angle. We need to convert the angle to radian as Visual Basic 2015 cannot deal with an angle in degree. The conversion is based on the following equation:<\/p>\n<p>\u03c0 radian= 180\u00ba<\/p>\n<p>so 1\u00ba=\u03c0\/180 radian<\/p>\n<p>The issue is how to get the exact value of\u00a0\u03c0? We can use\u00a0\u03c0=3.14159 but it will not be accurate. To get the exact value of\u00a0\u03c0, we use the arc sine function, i.e. is Asin.<\/p>\n<p>Using the equation \u00a0 sin(\u03c0\/2)=1, so Asin(1)=\u03c0\/2, therefore,\u00a0<strong>\u03c0=2Asin(1)<\/strong><\/p>\n<p>The syntax of \u00a0the Sin function in Visual Basic 2015 is<\/p>\n<p><strong>Math.Sin(Angle in radian)<\/strong><\/p>\n<h4><strong>Example 19.1<\/strong><\/h4>\n<p>In this example, we use pi to represent\u00a0\u03c0 and assign the\u00a0value of\u00a0\u03c0 using the formula\u00a0pi = 2*Math.Asin(1). We use the function Round to round the value of sine to four decimal places.<\/p>\n<pre style=\"font-size: 110%;\">Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click\r\nDim pi As Single\r\npi = 2*Math.Asin(1)\r\nMsgBox(\"Sin 90 is\" &amp; Math.Round(Math.Sin(pi \/ 2), 4))\r\nEnd Sub\r\n<\/pre>\n<h4>The Output<\/h4>\n<p style=\"text-align: center;\"><a href=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6538\" src=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.1.jpg\" alt=\"vb2015_fig19.1\" width=\"251\" height=\"155\" \/><\/a><strong>Figure 19.1<\/strong><\/p>\n<p><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script><br \/>\n<ins class=\"adsbygoogle\" style=\"display: block; text-align: center;\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\" data-ad-client=\"ca-pub-3033628290023372\" data-ad-slot=\"4768455349\"><\/ins><br \/>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/p>\n<h2><strong>19.2 The Cos function<\/strong><\/h2>\n<p>In Visual Basic 2015, the <strong>Cos<\/strong> function returns the Cosine value of an angle. The syntax is<\/p>\n<p><strong>Math.Cos(Angle in radian)<\/strong><\/p>\n<h4><strong>Example 19.2<\/strong><\/h4>\n<pre style=\"font-size: 110%;\">Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click\r\nDim pi As Single\r\npi = 2*Math.Asin(1)\r\nMsgBox(\"Cos 180 is \" &amp; Math.Round(Math.Cos(pi), 4))\r\nEnd Sub\r\n<\/pre>\n<h4>\u00a0The Output<\/h4>\n<p><a href=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.2.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6541\" src=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.2.jpg\" alt=\"vb2015_fig19.2\" width=\"251\" height=\"155\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><strong>Figure 19.2<\/strong><\/p>\n<p><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script><br \/>\n<ins class=\"adsbygoogle\" style=\"display: block; text-align: center;\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\" data-ad-client=\"ca-pub-3033628290023372\" data-ad-slot=\"4768455349\"><\/ins><br \/>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/p>\n<h2><strong>19.3 The Tan\u00a0function<\/strong><\/h2>\n<p style=\"text-align: left;\">In Visual Basic 2015, the Tan function returns the tangent\u00a0value of an angle. The syntax is<\/p>\n<p style=\"text-align: left;\"><strong>Math.Tan(Angle in radian)<\/strong><\/p>\n<p style=\"text-align: left;\"><strong>Example 19.3<\/strong><\/p>\n<pre style=\"font-size: 110%;\">Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click\r\nDim pi As Single\r\npi = 2 * Math.Asin(1)\r\nMsgBox(\"Tan 45 is \" &amp; Math.Round(Math.Tan(pi \/ 4)), 4)\r\nEnd Sub<\/pre>\n<p style=\"text-align: left;\"><strong>The Output<\/strong><\/p>\n<p style=\"text-align: left;\"><a href=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.3.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6543\" src=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.3.jpg\" alt=\"vb2015_fig19.3\" width=\"251\" height=\"155\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><strong>Figure 19.3<\/strong><\/p>\n<p><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script><br \/>\n<ins class=\"adsbygoogle\" style=\"display: block;\" data-ad-format=\"autorelaxed\" data-ad-client=\"ca-pub-3033628290023372\" data-ad-slot=\"1492877908\"><\/ins><br \/>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/p>\n<h2 style=\"text-align: left;\"><strong>19.4 The Asin Function<\/strong><\/h2>\n<p>The Asin function returns the value of arcsine (inverse sine ) and it represents the angle that corresponds to the sine value. For example, sin90\u00ba = 1, \u00a0so asin(1)=90\u00ba<\/p>\n<p>In Visual Basic 2015, the value of arcsine is expressed in terms of radian. To convert the value to degree, we use the formula 1 radian=180\u00ba\/\u03c0, where\u00a0\u03c0=2Asin(1).<\/p>\n<h4><strong>Example 19.4<\/strong><\/h4>\n<pre style=\"font-size: 110%;\">Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button7.Click\r\nDim pi As Single\r\npi = 2 * Math.Asin(1)\r\nMsgBox(\"Asin(1)is \" &amp; Math.Round(Math.Asin(1) * 180 \/ pi), 4)\r\nEnd Sub\r\n<\/pre>\n<p>The Output<\/p>\n<p><a href=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.4.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6547\" src=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.4.jpg\" alt=\"vb2015_fig19.4\" width=\"251\" height=\"155\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><strong>Figure 19.4<\/strong><\/p>\n<h2 style=\"text-align: left;\"><strong>19.5 The Acos Function<\/strong><\/h2>\n<p>In Visual Basic 2015, the Acos function returns the value of arc cosine (inverse cosine ) and it represents the angle that corresponds to the cos value. For example, cos90\u00ba = 0, \u00a0so acos(0)=90\u00ba<\/p>\n<p>&nbsp;<\/p>\n<h4><strong>Example 19.5<\/strong><\/h4>\n<pre style=\"font-size: 110%;\">Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button7.Click\r\nDim pi As Single\r\npi = 2 * Math.Asin(1)\r\nMsgBox(\"Asin(1)is \" &amp; Math.Round(Math.Acos(1) * 180 \/ pi), 4)\r\nEnd Sub\r\n<\/pre>\n<p><a href=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.5.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6549\" src=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.5.jpg\" alt=\"vb2015_fig19.5\" width=\"251\" height=\"155\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><strong>Figure 19.5<\/strong><\/p>\n<h2 style=\"text-align: left;\"><strong>19.6 The Atan Function<\/strong><\/h2>\n<p>In Visual Basic 2015, the Atan function returns the value of arc tangent\u00a0(inverse tangent) and it represents the angle that corresponds to the tan value. For example, tan45\u00ba = 1, \u00a0so atan(1)=45\u00ba<\/p>\n<h4><strong>Example 19.6<\/strong><\/h4>\n<pre style=\"font-size: 110%;\">Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button7.Click\r\nDim pi As Single\r\npi = 2 * Math.Asin(1)\r\nMsgBox(\"Asin(1)is \" &amp; Math.Round(Math.Atan(1) * 180 \/ pi), 4)\r\nEnd Sub\r\n<\/pre>\n<p><strong>The Output<\/strong><\/p>\n<p><a href=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.6.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6552\" src=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.6.jpg\" alt=\"vb2015_fig19.6\" width=\"251\" height=\"155\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><strong>Figure 19.6\u00a0<\/strong><\/p>\n<h2>\u00a0<strong>19.7 Applications<\/strong><\/h2>\n<p>Trigonometric\u00a0functions can be used to solve various mathematical problems. Common examples are problems involving the sine rule, the cosine rule, trigonometric identities, trigonometric equations, the projectile equation and more.<\/p>\n<h4><strong>Example 19.7 The Sine Rule<\/strong><\/h4>\n<p>For example, in a triangle ABC, give angle \u00a0A=60 and angle B=30 respectively, length BC denoted by a=4 \u00a0you can calculate length AC (denoted by b).<\/p>\n<p>The formula is<\/p>\n<p>a\/sinA=b\/sinB, so b=asinB\/sinA<\/p>\n<pre style=\"font-size: 110%;\">Private Sub Button8_Click(sender As Object, e As EventArgs) Handles Button8.Click\r\nDim pi As Single\r\n\r\nDim A As Single, B As Single, x As Single\r\n\r\npi = 2 * Math.Asin(1)\r\nA = 60 * pi \/ 180\r\nB = 40 * pi \/ 180\r\nx = 4\r\n\r\nMsgBox(\"AC= \" &amp; Math.Round((x * Math.Sin(A) \/ Math.Sin(B)), 4))\r\n\r\nEnd Sub\r\n<\/pre>\n<p><strong>The Output<\/strong><\/p>\n<p style=\"text-align: center;\">\u00a0<a href=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.7.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-6555\" src=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.7.jpg\" alt=\"vb2015_fig19.7\" width=\"154\" height=\"155\" srcset=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.7.jpg 154w, https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.7-150x150.jpg 150w\" sizes=\"auto, (max-width: 154px) 100vw, 154px\" \/><\/a><strong>Figure 19.7<\/strong><\/p>\n<p><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js\"><\/script><br \/>\n<ins class=\"adsbygoogle\"\n     style=\"display:block\"\n     data-ad-format=\"autorelaxed\"\n     data-ad-client=\"ca-pub-3033628290023372\"\n     data-ad-slot=\"5090773108\"><\/ins><br \/>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/p>\n<h4 style=\"text-align: center;\"><strong><a title=\"visual basic 2015 tutorial lesson 18\" href=\"http:\/\/www.vbtutor.net\/index.php\/visual-basic-2015-lesson-18-working-math-functions\/\">[Lesson 18]<\/a>&lt;&lt;<a title=\"visual basic 2015 tutorial\" href=\"http:\/\/www.vbtutor.net\/index.php\/visual-basic-2015-tutorial\/\">[Contents]<\/a>&gt;&gt;<a href=\"http:\/\/www.vbtutor.net\/index.php\/visual-basic-2015-lesson-20-format-functions\/\">[Lesson 20]<\/a><\/strong><\/h4>\n","protected":false},"excerpt":{"rendered":"<p>[Lesson 18]&lt;&lt;[Contents]&gt;&gt;[Lesson 20] In the previous lesson, we have learned how to write code using various mathematical functions in Visual Basic 2015. In this lesson, we shall proceed to learn how to work with a group of mathematical functions that deal with angles and lengths of a triangle, they are the trigonometric functions. The three &hellip; <a href=\"https:\/\/www.vbtutor.net\/index.php\/visual-basic-2015-lesson-19-trigonometric-functions\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Visual Basic 2015 Lesson 19: Trigonometric Functions<\/span><\/a><\/p>\n","protected":false},"author":23013,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-6533","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Visual Basic 2015 Lesson 19: Trigonometric Functions - Learn Visual Basic Programming \u2013 VB.NET, VBA &amp; Classic VB<\/title>\n<meta name=\"description\" content=\"This article describe how to work with trigonometric functions in visual basic 2015\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/www.vbtutor.net\/vb2015\/vb2015_lesson19.html\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Visual Basic 2015 Lesson 19: Trigonometric Functions - Learn Visual Basic Programming \u2013 VB.NET, VBA &amp; Classic VB\" \/>\n<meta property=\"og:description\" content=\"This article describe how to work with trigonometric functions in visual basic 2015\" \/>\n<meta property=\"og:url\" content=\"http:\/\/www.vbtutor.net\/vb2015\/vb2015_lesson19.html\" \/>\n<meta property=\"og:site_name\" content=\"Learn Visual Basic Programming \u2013 VB.NET, VBA &amp; Classic VB\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Vbtutor\" \/>\n<meta property=\"article:modified_time\" content=\"2018-06-22T10:11:42+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.1.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@liewvk\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.vbtutor.net\/index.php\/visual-basic-2015-lesson-19-trigonometric-functions\/\",\"url\":\"http:\/\/www.vbtutor.net\/vb2015\/vb2015_lesson19.html\",\"name\":\"Visual Basic 2015 Lesson 19: Trigonometric Functions - Learn Visual Basic Programming \u2013 VB.NET, VBA &amp; Classic VB\",\"isPartOf\":{\"@id\":\"https:\/\/www.vbtutor.net\/#website\"},\"primaryImageOfPage\":{\"@id\":\"http:\/\/www.vbtutor.net\/vb2015\/vb2015_lesson19.html#primaryimage\"},\"image\":{\"@id\":\"http:\/\/www.vbtutor.net\/vb2015\/vb2015_lesson19.html#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.1.jpg\",\"datePublished\":\"2015-04-08T05:27:10+00:00\",\"dateModified\":\"2018-06-22T10:11:42+00:00\",\"description\":\"This article describe how to work with trigonometric functions in visual basic 2015\",\"breadcrumb\":{\"@id\":\"http:\/\/www.vbtutor.net\/vb2015\/vb2015_lesson19.html#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"http:\/\/www.vbtutor.net\/vb2015\/vb2015_lesson19.html\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"http:\/\/www.vbtutor.net\/vb2015\/vb2015_lesson19.html#primaryimage\",\"url\":\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.1.jpg\",\"contentUrl\":\"https:\/\/www.vbtutor.net\/wordpress\/wp-content\/uploads\/2015\/04\/vb2015_fig19.1.jpg\",\"width\":251,\"height\":155},{\"@type\":\"BreadcrumbList\",\"@id\":\"http:\/\/www.vbtutor.net\/vb2015\/vb2015_lesson19.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.vbtutor.net\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Visual Basic 2015 Lesson 19: Trigonometric Functions\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.vbtutor.net\/#website\",\"url\":\"https:\/\/www.vbtutor.net\/\",\"name\":\"Learn Visual Basic Programming \u2013 VB.NET, VBA &amp; Classic VB\",\"description\":\"Start learning Visual Basic from beginner to advanced. 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