Question

Write cot(0) in terms of sin(0) if 0 is in quadrant 2

Answer 1

Cot (θ) in term of sin (θ) is cot (θ) = ± √ [  1 - sin² (θ) ]  / sin (θ)

A trignometric function, sometimes known as a circular function, is a function of an arc or angle that is most easily described in terms of the ratios of pairs of sides of a right-angled triangle. Examples of such functions are the sine, cosine, tangent, cotangent, secant, or cosecant.

The trigonometric function cot (θ) can be written as:

cot (θ) = cos (θ) / sin (θ)

Now by using the Pythagorean identity,

sin² (θ) + cos² (θ) = 1

cos² (θ) = 1 - sin² (θ)

cos (θ) = ± √ [  1 - sin² (θ) ]

Therefore, substituting the value of cos (θ) in the expression of cot (θ).

cot (θ) = cos (θ) / sin (θ)

cot (θ) = ± √ [  1 - sin² (θ) ]  / sin (θ)

Now, cos (θ) < 0 because the angle θ is in the second quadrant,

Therefore,

cos (θ) = - √ [  1 - sin² (θ) ]

Hence,

cot (θ) = - √ [  1 - sin² (θ) ]  / sin (θ)

Learn more about quadrants here:

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