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:
brainly.com/question/25038683
#SPJ9
