Trigonometry

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Trigonometric identities

The following equations are the most basic and important trigonometric identities. These equations are true for any angle. From them, countless additional identities can be formed.

Basic trigonometric identities:

tanθ

=

sinθ
cosθ

cotθ

=

_1_
tanθ

secθ

=

_1_
cosθ

cscθ

=

_1_
sinθ

triángulo

Pythagorean Identities:
a) sin²A + cos² A = 1
b) 1 + tg² A = sec²A
c) 1 + cot² A = csc²A

You can use the trigonometric identities given above to find trigonometric ratios if you are given the quadrant an angle lies in and the value of one trigonometric ratio.

It will be useful to remember the sign of the trigonometric ratios in each quadrant:

signos

If sinθ= $\frac{3}{5}$ and , find cosθ and tanθ.

cos²θ=1-sin²θ=1-( $\frac{3}{5}$ )²= $\frac{16}{25}$ , then cosθ=- $\frac{4}{5}$ because