Question

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.

Answer 1

Answer:

+√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