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)=(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

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

Part 3

Find out the value of tan(theta)

`\tan (\theta)=(\sin (\theta))/(\cos (\theta))`

substitute given values

`\tan (\theta)=(24)/(7)`