Pythagorean Identities
*There are three so-called “Pythagorean Identities” that can be used to simplify expressions containing trigonometric functions. The three Pythagorean identities are:
sin2x + cos2x = 1
1 + cot2x = csc2x
tan2x + 1 = sec2x
*These identities can be used to determine function values.
Example: If the cot x = √3 2 , then what is the value of csc x if the angle is in Quadrant 3?
Using the second Pythagorean identity, we substitute the given value for cot x.
1 +
(
√3
2
)
2
=
csc2x
1 + 3 4 = csc2x
7 4 = csc2x
−√7 2 = csc x
(The csc function is negative in quadrant 3.)
1 + 3 4 = csc2x
7 4 = csc2x
−√7 2 = csc x
(The csc function is negative in quadrant 3.)
