Question

If sin theta = 1/4 and theta is in quadrant ii, find the exact value of sin(theta-pi/3)

Answer 1

To find the exact value of sin(theta - pi/3), use the trigonometric identity sin(A - B) = sin(A)cos(B) - cos(A)sin(B). Substitute the given values of sin(theta), cos(theta), and pi/3 into the identity to find the exact value.

Step-by-step explanation:

To find the exact value of sin(theta - pi/3), we can use the trigonometric identity sin(A - B) = sin(A)cos(B) - cos(A)sin(B). In this case, A = theta and B = pi/3.

Given that sin(theta) = 1/4, we can determine the values of sin(theta) and cos(theta) using the Pythagorean identity sin^2(theta) + cos^2(theta) = 1.

Using this information, we can substitute the values of sin(theta), cos(theta), and pi/3 into the trigonometric identity to find the exact value of sin(theta - pi/3).

Answer 2

To get the value required we proceed as follow:
sin θ=1/4
θ = arcsin 1/4
θ=14.4775~14.5°
Since it is in the quadrant ii, the value of θ=180-14.5=165.5°
Answer: 165.5°