Question

Given sin(0) = -1/4 and tan 0 = squareroot of 15/15. what is the value of cos 0?

Answer 1

Answer:

$\cos \theta = \frac{\sqrt{15}}{4}}$

Step-by-step explanation:

Recall that $\sin(-\theta)=-\sin(\theta)$. Therefore, $\sin\theta=-(-\frac{1}{4})=\frac{1}{4}$

In any right triangle:

• The sine of an angle is equal to its opposite side divided by the hypotenuse of the triangle (o/h)

• The cosine of an angle is equal to its adjacent side divided by the hypotenuse of the triangle (a/h)

• The tangent of an angle is equal to its opposite side divided by its adjacent side (o/a)

From $\sin \theta=\frac{1}{4}$ and $\tan \theta = \frac{\sqrt{15}}{15}$, we know:

• $\theta$'s opposite side is 1
• $\theta$'s adjacent side is $\sqrt{15}$
• The hypotenuse of the triangle is 4

Therefore, the desired answer is $\boxed{\cos \theta = \frac{\sqrt{15}}{4}}}$.