Question

Use the quotient and reciprocal identities to find cotθ exactly given:

sinθ = -13/20
cosθ = -√231/20

a. cotθ = 20/13
b. cotθ = -20/13
c. cotθ = -13/√231
d. cotθ = -√231/13

Answer 1

To find the exact value of cotθ, we use the provided values of sinθ and cosθ to calculate cotθ = cosθ/sinθ, which simplifies to -√231/13.

Step-by-step explanation:

The student asks for the exact value of cotθ given that sinθ = -13/20 and cosθ = -√231/20. The cotangent of an angle θ, or cotθ, is the reciprocal of the tangent of θ, which also equals the cosine of θ divided by the sine of θ (cotθ = cosθ/sinθ). Substituting the provided values, we find that cotθ = (-√231/20) / (-13/20), which simplifies to cotθ = √231/13. Hence, the correct answer is cotθ = -√231/13.