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?

Question

Mathematics

Alonzo Cantu

3 April, 08:05

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?

+4

Answers (1)

Know the Answer?

Claire Knight · Answer 1

(√55) / 8

Step-by-step 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