# How would you find the exact value of the six trigonometric function of 120 degrees?

On the Cartesian Plane, an angle of 120° lies in the second quadrant.

the six trig ratios are defined as

Notice that the three ratios on the right are reciprocals of the three on the left.

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To find the exact values of the six trigonometric functions of 120 degrees, you can use the unit circle. First, identify the point on the unit circle corresponding to 120 degrees. Then, calculate the sine, cosine, tangent, cosecant, secant, and cotangent of that angle. Here are the exact values:

- Sine (sin): √3 / 2
- Cosine (cos): -1 / 2
- Tangent (tan): -√3
- Cosecant (csc): 2 / √3
- Secant (sec): -2
- Cotangent (cot): -1 / √3

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