{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T20:24:19+00:00","modifiedTime":"2022-08-11T14:22:45+00:00","timestamp":"2022-09-14T18:19:53+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Trigonometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33729"},"slug":"trigonometry","categoryId":33729}],"title":"Express Sine in Terms of Tangent","strippedTitle":"express sine in terms of tangent","slug":"express-sine-in-terms-of-tangent","canonicalUrl":"","seo":{"metaDescription":"Learn how to express sine in terms of tangent in this trigonometry article including step-by-step instructions.","noIndex":0,"noFollow":0},"content":"Even though each trigonometry function is perfectly wonderful, being able to express each trig function in terms of one of the other five trig functions is frequently to your advantage. For example, you may have some sine terms in an expression that you want to express in terms of tangent, so that all the functions match, making it easier to solve the equation.\r\n\r\nTo rewrite the sine function in terms of tangent, follow these steps:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Start with the ratio identity involving sine, cosine, and tangent, and multiply each side by cosine to get the sine alone on the left.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/274240.image0.png\" alt=\"image0.png\" width=\"117\" height=\"67\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Replace cosine with its reciprocal function.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/274241.image1.png\" alt=\"image1.png\" width=\"129\" height=\"48\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Solve the Pythagorean identity tan<sup>2</sup>θ + 1 = sec<sup>2</sup>θ for secant.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/274242.image2.png\" alt=\"image2.png\" width=\"293\" height=\"31\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Replace the secant in the sine equation.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/274243.image3.png\" alt=\"image3.png\" width=\"383\" height=\"56\" /></li>\r\n</ol>","description":"Even though each trigonometry function is perfectly wonderful, being able to express each trig function in terms of one of the other five trig functions is frequently to your advantage. For example, you may have some sine terms in an expression that you want to express in terms of tangent, so that all the functions match, making it easier to solve the equation.\r\n\r\nTo rewrite the sine function in terms of tangent, follow these steps:\r\n<ol class=\"level-one\">\r\n \t<li>\r\n<p class=\"first-para\">Start with the ratio identity involving sine, cosine, and tangent, and multiply each side by cosine to get the sine alone on the left.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/274240.image0.png\" alt=\"image0.png\" width=\"117\" height=\"67\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Replace cosine with its reciprocal function.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/274241.image1.png\" alt=\"image1.png\" width=\"129\" height=\"48\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Solve the Pythagorean identity tan<sup>2</sup>θ + 1 = sec<sup>2</sup>θ for secant.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/274242.image2.png\" alt=\"image2.png\" width=\"293\" height=\"31\" /></li>\r\n \t<li>\r\n<p class=\"first-para\">Replace the secant in the sine equation.</p>\r\n<img src=\"https://www.dummies.com/wp-content/uploads/274243.image3.png\" alt=\"image3.png\" width=\"383\" height=\"56\" /></li>\r\n</ol>","blurb":"","authors":[{"authorId":8985,"name":"Mary Jane Sterling","slug":"mary-jane-sterling","description":" <p><b>Mary Jane Sterling</b> is the author of <i>Algebra I For Dummies, Algebra Workbook For Dummies,</i> and many other <i>For Dummies</i> books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics. 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Express Sine in Terms of Tangent

By: Mary Jane Sterling and

Updated: 08-11-2022

Trigonometry For Dummies

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Even though each trigonometry function is perfectly wonderful, being able to express each trig function in terms of one of the other five trig functions is frequently to your advantage. For example, you may have some sine terms in an expression that you want to express in terms of tangent, so that all the functions match, making it easier to solve the equation.

To rewrite the sine function in terms of tangent, follow these steps:

Start with the ratio identity involving sine, cosine, and tangent, and multiply each side by cosine to get the sine alone on the left.
Replace cosine with its reciprocal function.
Solve the Pythagorean identity tan²θ + 1 = sec²θ for secant.
Replace the secant in the sine equation.

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Express Sine in Terms of Tangent

Trigonometry For Dummies

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