Question

Consider this equation, tan⁡(θ) = 3√5/2, and θ is an angle in quadrant I, what is the value of cos⁡(θ)?

a. -3√7
b. 3√7
c. 2/√5
d. -2/√5

Answer 1

To find the value of cos(θ), use the identity cos²(θ) + sin²(θ) = 1 and the Pythagorean identity sec²(θ) = 1 + tan²(θ). Plug in the given value to find the value of sec²(θ) and then take the square root to find sec(θ).

Step-by-step explanation:

To find the value of cos(θ), we can use the identity: cos²(θ) + sin²(θ) = 1. Since tan(θ) = 3√5/2, we can use the Pythagorean identity: sec²(θ) = 1 + tan²(θ) to find the value of cos²(θ). Plugging in the given value, we get sec²(θ) = 1 + (3√5/2)².

Simplifying, sec²(θ) = 1 + 45/4 = 49/4. Taking the square root of both sides, we get sec(θ) = ±7/2. Since θ is in quadrant I, cos(θ) is positive, so we take the positive value of sec(θ), which is 7/2.