Question

Find sin of theta when you only know cos of theta. You have to use the Pythagorean Identity!

Answer 1

`\huge\boxed{B. \ sin \theta = (√(35) )/(6) }`

Explanation:

We'll use the following Pythagorean Identity:

`cos ^ 2 \theta + sin^2 \theta = 1`

Finding sin θ , we'll rearrange the formula as:

`sin \theta = √(1 - cos^2 \theta)`

Given that cos θ = - 1 / 6

`sin \theta = \sqrt{1 - (-(1)/(6) )^2} \\sin \theta = \sqrt{1-(1)/(36) } \\sin \theta = \sqrt{(36-1)/(36) } \\sin \theta = \sqrt{(35)/(36) } \\sin \theta = (√(35) )/(√(36) )\\ sin \theta = (√(35) )/(6)`