Online Test Banks
Score higher
See Online Test Banks
eLearning
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

Express Sine in Terms of Secant or Cosecant

Even though each trig 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 secant or cosecant, so that all the functions match, making it easier to solve the equation.

The easiest way to do this is to start with the Pythagorean identity,

image0.png

solve for the sine in terms of cosine and replace each cosine with 1 over its reciprocal (which is secant):

image1.png

The radical has a fraction in it. A better form is to simplify that fraction, so find a common denominator and split the fraction into two radicals — the bottom one of which you can further simplify:

image2.png

The last function to write sine in terms of is the cosecant. The reciprocal of cosecant is sine, so this equation is just one of the basic reciprocal identities:

image3.png
  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Advertisement

Inside Dummies.com

Dummies.com Sweepstakes

Win $500. Easy.