Question

Find the exact values of the remaining trigonometric functions of θ satisfying the given conditions. (If an answer is undefined, enter UNDEFINED.)

tan θ is undefined, π ≤ θ ≤ 2π

sin θ =

Answer 1

To find the exact values of the trigonometric functions of θ satisfying the given conditions, we need to determine the values of sin θ, cos θ, tan θ, cosec θ, sec θ, and cot θ. Since tan θ is undefined in the given range, this means that cos θ = 0. Therefore, the values of θ that satisfy the given conditions are π/2 and 3π/2.

Step-by-step explanation:

To find the exact values of the remaining trigonometric functions of θ satisfying the given conditions, we need to determine the values of sin θ, cos θ, tan θ, cosec θ, sec θ, and cot θ. Since tan θ is undefined in the given range, this means that cos θ = 0. We know that cos θ = 0 when θ is equal to π/2 or 3π/2. Therefore, the values of θ that satisfy the given conditions are π/2 and 3π/2.

Since cos θ = 0, this means that sin θ = 1 and cosec θ = 1/sin θ = 1/1 = 1. The remaining trigonometric functions, sec θ and cot θ, are undefined in this case.