Question

Let , −3−8 be a point on the terminal side of θ . find the exact values of sinθ , cscθ , and cotθ .

Answer 1

If ( -3, - 8 ) is the point on the terminal side of this angle:
cot (theta) = - 3/( - 8 ) = 3/8
cos (theta) / sin (theta) = 3/8
cos (theta) = 3 sin(theta)/8
sin² (theta) + cos² (theta) = 1
Therefore: sin ²(theta) + (3 sin(theta) /8 )² = 1
sin²(theta) + 9sin²(theta) / 64 = 1 /*64
64 sin² (theta) + 9 sin² (theta) = 64
73 sin² (theta) = 64
sin(theta) = √ (64/73) = - 8 / √73
csc (theta) = 1 / sin(theta) = 1 / (- 8/√73 ) = -√73 / 8