Question

Determine the value of θ to the nearest degree if 0° ≤ θ ≤ 360° for csc θ = 1.6406.

a) 22°
b) 57°
c) 78°
d) 174°

Answer 1

To find the value of θ, use the reciprocal trigonometric function of csc, which is sin, and find the inverse sine of 1.6406 using a calculator. The value of θ to the nearest degree is 57°. Hence the correct answer is option B

Step-by-step explanation:

To find the value of θ, we can use the reciprocal trigonometric function of csc, which is sin. The equation sin(θ) = 1.6406 is given.

To solve for θ, we can take the inverse sine of both sides: θ = sin-1(1.6406).

Using a calculator, we find that sin-1(1.6406) is approximately 57.04 degrees.

Therefore, the value of θ to the nearest degree is 57°.

Hence the correct answer is option B