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Trigonometry
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

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:

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

If the secant of an angle is -1 and the angle is in the second quadrant