Question

The angle \theta_1θ 1 ​ theta, start subscript, 1, end subscript is located in Quadrant \text{I}Istart text, I, end text, and \cos(\theta_1)=\dfrac{3}{8}cos(θ 1 ​ )= 8 3 ​ cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, start fraction, 3, divided by, 8, end fraction . What is the value of \sin(\theta_1)sin(θ 1 ​ )sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis?

Answer 1

(√55)/8

Explanation:

The sine and cosine are related by ...

sin² +cos² = 1

Then the sine of the angle is ...

sin(θ₁) = √(1 -cos(θ₁)²)

sin(θ₁) = √(1 - (3/8)²) = √(55/64)

sin(θ₁) = (√55)/8