Question

Given sin (-theta) = 1/5 and tan theta = sqrt.6/12

Answer 1

Given  $sin (\theta) = \frac{1}{5}$, and$tan \theta = \frac{\sqrt{6} }{12}$, then:

$cos\theta=\frac{2\sqrt{6} }{5}$

Computations on trigonometric identities

From the details provided:

$sin (\theta) = \frac{1}{5}\ \\\\tan \theta = \frac{\sqrt{6} }{12} \times \frac{\sqrt{6} }{\sqrt{6} }\\\\tan \theta = \frac{\sqrt{6} \times \sqrt{6} }{12 \times \sqrt{6} }\\\\tan \theta =\frac{1}{2\sqrt{6} }$

From the relationship above:

Opposite = 1

Adjacent = $2\sqrt{6}$

Hypotenuse = 5

$cos\theta=\frac{Adjacent}{Hypotenuse} \\\\cos\theta=\frac{2\sqrt{6} }{5}$

Learn more on trigonometry here: brainly.com/question/20519838