Question

Given that cos(θ) = 5/6, what is the value of tan(θ)?

A. 5/6
B. 6/5
C. 11/6
D. √11/6

Answer 1

To find the value of tan(θ) given cos(θ) = 5/6, we use the Pythagorean identity to find sin(θ), then divide sin(θ) by cos(θ) to get tan(θ) which is √11/6.

Step-by-step explanation:

Given that cos(θ) = 5/6, to find the value of tan(θ), we must use the Pythagorean identity which relates the sine, cosine, and tangent of an angle. The identity states that:

sin²(θ) + cos²(θ) = 1

We already have the cosine of the angle, so we can find the sine:

sin(θ) = √(1 - cos²(θ))

sin(θ) = √(1 - (5/6)²)

sin(θ) = √(1 - 25/36)

sin(θ) = √(36/36 - 25/36)

sin(θ) = √(11/36)

sin(θ) = √11/6

Now, we can calculate the tangent which is the sine over the cosine:

tan(θ) = sin(θ) / cos(θ)

tan(θ) = (√11/6) / (5/6)

Therefore, the value of tan(θ) is √11/6, which corresponds to answer choice D.