4.3 Right Triangle Trigiometry

Section three of chapter four has to do with trigonometric identities, and how they can be manipulated to create other identities.

An identity is defined as being an equation that for every possible input for the variables, the equation is true. In dealing with trigonometric functions, the variable is quite often theta.

Some basic trig. identities are the reciprocal identities, which express the relationship of sin, cos, and tan, and their respective inverses.

Quotient identities have to do with the relationship between cot and tan, with sin and cos.
 

The even/odd identities show whether each trig. function is even or odd.

Even/Odd Identities



Note: cos and sec are the only odd functions; the rest are even.

The next group of identities is referred to as the 'Pythagorean Identities', and can only be truly understood when understanding how they are derived from a right triangle.

 

 

(Pythagorean theorem)


<------Most important Pythagorean identity

From the equation above, the other two Pythagorean identities can be derived.

Pythagorean Identities









Application

When solving problems using the identities listed above, one if often asked to manipulate one side of the equation. It is probably in one's best interest to work on the more complicated side to get the simpler identity on the other side.

There is no one, correct way to do these problems, so one can be creative with their work.

Examples: