Question

Use a calculator to solve for θ in the given interval. Cot θ= 0.7615, for 0 < θ < 2 pi

Answer 1

θ = 52.71° or 232.71°

In radians

θ = 0.2928π rad or 1.2928π rad

That is,

θ = 0.92 rad or 4.06 rad

Step-by-step explanation:

Cot θ = 0.7615 for 0 ≤ θ ≤ 2π

Note that Cot θ = (1/tan θ)

(1/tan θ) = 0 7615

tan θ = (1/0.7615) = 1.3132

θ = tan⁻¹ (1.3132) = 52.71°

But, note that tan is also positive in the 3rd quadrant, hence,

θ is also equal to 180° + 52.71° = 232.71°

θ = 52.71° or 232.71°

We now convert to radians

360° = 2π

52.71° = (52.71 × 2π)/360 = 0.2928π = 0.92 radian

232.71° = (232.71 × 2π)/360 = 1.2928π = 4.06 radians