Right Triangle Trigonometry

Equations that are always true are called identities.

Trigonometric Functions, when theta is an acute angle of a right triangle:

 

 

Reciprocal Identities

 Quotient Identities

Even/Odd Functions: With trigonometric functions, some are odd, while others are even.
Odd:

Even:

Cofunction identities: Since theta and the other acute angle equal 90 degrees, subtracting the theta angle from pi/2 gets you the measurement of the other angle. 

Deriving Pythagorean Identities

We now know that  is true, so we can use that to find the two other Pythagorean identities.

And the final one:

Pythagorean Identities

Measurements of Special Angles on the Unit Circle

Verifying Trigonometric Identities

To verify an identity, you can use any of the identity "rules" as mentioned above. However, you may only work on ONE side of the equation.

    Use the quotient identities.

 Give both fractions a common denominator, and combine.

         Based off the pythagorean identity, the top equals 1. The reciprocals of the denominator can be found, which verifies the identity.