Quotient Identities
|
![](/math/trigonometry/images/quotient_identities_3.gif)
![](/math/trigonometry/images/quotient_identities_4.png)
![](/math/trigonometry/images/quotient_identities_5.png)
![](/math/trigonometry/images/quotient_identities_6.png)
Substitute the appropriate values into the identity and simplify:
![](/math/trigonometry/images/quotient_identities_7.png)
![](/math/trigonometry/images/quotient_identities_8.png)
![](/math/trigonometry/images/quotient_identities_9.png)
![](/math/trigonometry/images/quotient_identities_10.png)
![](/math/trigonometry/images/quotient_identities_11.png)
Let's look at the cotangent quotient identity using a familiar 45-45-90 triangle.
![](/math/trigonometry/images/quotient_identities_12.gif)
![](/math/trigonometry/images/quotient_identities_13.png)
![](/math/trigonometry/images/quotient_identities_14.png)
![](/math/trigonometry/images/quotient_identities_15.png)
Substitute the appropriate values into the identity and simplify:
![](/math/trigonometry/images/quotient_identities_16.png)
![](/math/trigonometry/images/quotient_identities_17.png)
![](/math/trigonometry/images/quotient_identities_18.png)
1 = 1
![](/math/trigonometry/images/quotient_identities_11.png)
The quotient identities will be used in trigonometric proofs and applications of calculus where using an identity is a more convenient form. Remember that the difference between an equation and an identity is that an identity will be true for ALL values.
Related Links: Math Trigonometry Pythagorean Identities Cofunction Identities |
To link to this Quotient Identities page, copy the following code to your site: