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A trigonometric ratio relates two side lengths of a right triangle. Consider the right triangle △ABC. One of its acute angles has been named θ.
Since it is opposite to the right angle, BC is the hypotenuse of the right triangle. The remaining sides — the legs — can be named relative to the marked angle θ. Because AB is next to ∠θ, it is called the adjacent side. Conversely, because AC lies across from ∠θ, it is called the opposite side.
Trigonometric ratios can be used to determine unknown side lengths or angle measures in right triangles.sinθ=HypotenuseOpposite
cosθ=HypotenuseAdjacent
tanθ=AdjacentOpposite
csc(θ)=oppositehypotenuse
sec(θ)=adjacenthypotenuse
cotθ=oppositeadjacent
θ | sinθ | cosθ | tanθ | |
---|---|---|---|---|
Degrees | Radians | |||
0 | 0 | 0 | 1 | 0 |
30 | 6π | 21 | 23 | 33 |
45 | 4π | 22 | 22 | 1 |
60 | 3π | 23 | 21 | 3 |
90 | 2π | 1 | 0 | undefined |
120 | 32π | 23 | -21 | -3 |
135 | 43π | 22 | -22 | -1 |
150 | 65π | 21 | -23 | -33 |
180 | π | 0 | -1 | 0 |
210 | 67π | -21 | -23 | 33 |
225 | 45π | -22 | -22 | 1 |
240 | 34π | -23 | -21 | 3 |
270 | 23π | -1 | 0 | undefined |
300 | 35π | -23 | 21 | -3 |
315 | 47π | -22 | 22 | -1 |
330 | 611π | -21 | 23 | -33 |
360 | 2π | 0 | 1 | 0 |