First slide

Trignometry

Question

Given that $\sin θ = \frac{1}{4} .$ Find the values of $\cos θ and \tan θ .$

Easy

A

$\frac{\sqrt{5}}{4}, \frac{1}{\sqrt{5}}$
B

$\frac{\sqrt{15}}{4}, 1$
C

$\frac{\sqrt{15}}{4}, \frac{1}{\sqrt{15}}$
D

$1, \frac{1}{\sqrt{15}}$

Solution

$In ∆ A B C, \sin θ = \frac{1}{4}$
AB=1 and AC=4
$B C = \sqrt{(4)^{2} - (1)^{2}} = \sqrt{15}$

$\cos θ = \frac{B C}{A C} = \frac{\sqrt{15}}{4}$
$\tan θ = \frac{A B}{B C} = \frac{1}{\sqrt{15}}$

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