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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.
sin θ=Opposite/Hypotenuse
cos θ=Adjacent/Hypotenuse
tan θ=Opposite/Adjacent
csc(θ)=hypotenuse/opposite
sec(θ)=hypotenuse/adjacent
cot θ =adjacent/opposite
θ | sin θ | cos θ | tan θ | |
---|---|---|---|---|
Degrees | Radians | |||
0 | 0 | 0 | 1 | 0 |
30 | π/6 | 1/2 | sqrt(3)/2 | sqrt(3)/3 |
45 | π/4 | sqrt(2)/2 | sqrt(2)/2 | 1 |
60 | π/3 | sqrt(3)/2 | 1/2 | sqrt(3) |
90 | π/2 | 1 | 0 | undefined |
120 | 2π/3 | sqrt(3)/2 | -1/2 | -sqrt(3) |
135 | 3π/4 | sqrt(2)/2 | -sqrt(2)/2 | -1 |
150 | 5π/6 | 1/2 | -sqrt(3)/2 | -sqrt(3)/3 |
180 | π | 0 | -1 | 0 |
210 | 7π/6 | -1/2 | -sqrt(3)/2 | sqrt(3)/3 |
225 | 5π/4 | -sqrt(2)/2 | -sqrt(2)/2 | 1 |
240 | 4π/3 | -sqrt(3)/2 | -1/2 | sqrt(3) |
270 | 3π/2 | -1 | 0 | undefined |
300 | 5π/3 | -sqrt(3)/2 | 1/2 | -sqrt(3) |
315 | 7π/4 | -sqrt(2)/2 | sqrt(2)/2 | -1 |
330 | 11π/6 | -1/2 | sqrt(3)/2 | -sqrt(3)/3 |
360 | 2π | 0 | 1 | 0 |