The angle / theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant / text{I}Istart text, I, end text, and / sin (/theta_1) = / dfrac{1}{2}sin (θ 1 ) = 2 1 sine, (, theta, start subscript, 1, end subscript,), equals, start fraction, 1, divided by, 2, end fraction. What is the value of / cos (/theta_1) cos (θ 1 ) cosine, (, theta, start subscript, 1, end subscript,) ? Express your answer exactly.

Question

Physics

Caitlin

5 February, 04:18

The angle / theta_1θ 1 theta, start subscript, 1, end subscript is located in Quadrant / text{I}Istart text, I, end text, and / sin (/theta_1) = / dfrac{1}{2}sin (θ 1 ) = 2 1 sine, (, theta, start subscript, 1, end subscript,), equals, start fraction, 1, divided by, 2, end fraction. What is the value of / cos (/theta_1) cos (θ 1 ) cosine, (, theta, start subscript, 1, end subscript,) ? Express your answer exactly.

+3

Answers (1)

Know the Answer?

Janelle Hebert · Answer 1

+√3/2

Explanation:

Here is the complete question

If θ is located in Quadrant 1 and sinθ = 1/2. What is the value of cosθ?

Solution

From sin²θ + cos²θ = 1

cosθ = ±√ (1 - sin²θ) = ±√ (1 - (1/2) ²) = ± (1 - 1/4) = ±√ (3/4) = ±√3/2

cosθ = ±√3/2.

Since θ is in Quadrant 1, we take the positive answer.

So, cosθ = + √3/2