Home

Express Sine in Terms of Tangent

|
|  Updated:  
2022-08-11 14:22:45
|   From The Book:  
No items found.
Trigonometry For Dummies
Explore Book
Buy On Amazon
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:

  1. Start with the ratio identity involving sine, cosine, and tangent, and multiply each side by cosine to get the sine alone on the left.

    image0.png
  2. Replace cosine with its reciprocal function.

    image1.png
  3. Solve the Pythagorean identity tan2θ + 1 = sec2θ for secant.

    image2.png
  4. Replace the secant in the sine equation.

    image3.png

About This Article

This article is from the book: 

No items found.

About the book author:

Mary Jane Sterling (Peoria, Illinois) is the author of Algebra I For Dummies, Algebra Workbook For Dummies, Algebra II For Dummies, Algebra II Workbook For Dummies, and many other For Dummies books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics.