Question

Find the values of sin, cos, and tan for the given right triangle. Give the exact values.

Answer 1

Part 1

Find out the value of sin(theta)

$\sin (\theta)=\frac{24}{25}$

By opposite side divided by the hypotenuse in a right triangle

Part 2

Find out cos(theta)

Remember that

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

substitute the value of sine

$(\frac{24}{25})^2+\cos ^2(\theta)=1$$\cos ^2(\theta)=1-\frac{576}{625}$$\begin{gathered} \cos ^2(\theta)=\frac{49}{625} \\ \\ \cos ^{}(\theta)=\frac{7}{25} \end{gathered}$

Part 3

Find out the value of tan(theta)

$\tan (\theta)=\frac{\sin (\theta)}{\cos (\theta)}$

substitute given values

$\tan (\theta)=\frac{24}{7}$