Question

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

Answer 1

Answer:

$\huge\boxed{B. \ sin \theta = \frac{\sqrt{35} }{6} }$

Step-by-step explanation:

We'll use the following Pythagorean Identity:

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

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

$sin \theta = \sqrt{1 - cos^2 \theta}$

Given that cos θ = - 1 / 6

$sin \theta = \sqrt{1 - (-\frac{1}{6} )^2} \\sin \theta = \sqrt{1-\frac{1}{36} } \\sin \theta = \sqrt{\frac{36-1}{36} } \\sin \theta = \sqrt{\frac{35}{36} } \\sin \theta = \frac{\sqrt{35} }{\sqrt{36} }\\ sin \theta = \frac{\sqrt{35} }{6}$