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

Answer 1

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

Using the associated right-angled triangle with sides of length #-1,sqrt3 and 2# for the sides, x, y and r respectively,

the six trig ratios are defined as

#sin 120° = y/r = sqrt3/2 and "cosec" 120° = r/y = 2/sqrt3#
#cos 120° = x/r = (-1)/2 and sec 120° = 2/(-1)#
#tan 120° = y/x = sqrt3/(-1) and cot 120° = (-1)/sqrt3#

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

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Answer 2

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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