Immediately, by definition of cotangent, we find
tan(α) = 1/cot(α) = 1/(-√3)
⇒ tan(α) = -√3
Given that π/2 < α < π, we know that cos(α) < 0 and sin(α) > 0. In turn, sec(α) < 0 and csc(α) > 0.
Recall the Pythagorean identity,
cos²(α) + sin²(α) = 1
Multiplying both sides by 1/sin²(α) recovers another form of the identity,
cot²(α) + 1 = csc²(α)
Solving for csc(α) above yields
csc(α) = + √(cot²(α) + 1) = √((-√3)² + 1) = √4
⇒ csc(α) = 2
⇒ sin(α) = 1/2
Solve for cos(α) using the first form of the Pythagorean identity:
cos(α) = - √(1 - sin²(α)) = - √(1 - (1/2)²) = - √(3/4)
⇒ cos(α) = -√3/2
⇒ sec(α) = -2/√3
, find the exact values of the five remaining trigonometric functions:
