Question

The angle [θ₁] is located in quadrant [i], and [sin(θ₁)=dfrac12] . what is the value of [cos(θ₁)]? express your answer exactly.

Answer 1

The value of cos(θ₁) is √3/2.

Step-by-step explanation:

Given that the angle θ₁ is located in quadrant I and that sin(θ₁) = 1/2, we can use the Pythagorean identity to find cos(θ₁). The Pythagorean identity states that sin²(θ) + cos²(θ) = 1. Since sin(θ₁) = 1/2, we can substitute 1/2 for sin(θ₁) in the equation and solve for cos(θ₁):

sin²(θ₁) + cos²(θ₁) = 1

(1/2)² + cos²(θ₁) = 1

1/4 + cos²(θ₁) = 1

cos²(θ₁) = 1 - 1/4 = 3/4

cos(θ₁) = √(3/4) = √3/2