Question

What are the sine, cosine, and tangent of 5 pi over 4 radians?

Answer 1

`\sin(5\pi)/(4)=-(1)/(√(2))`

`\cos(5\pi)/(4)=-(1)/(√(2))`

`\tan(5\pi)/(4)=1`

Explanation:

Given :
`\theta =(5\pi)/(4)`

The angle is on radian.

We need to find the sine, cosine and tangent.

`\sin\theta =\sin((5\pi)/(4)`

`\sin\theta =\sin(\pi+(\pi)/(4)`

`\sin\theta =-\sin((\pi)/(4)`
`\because \sin(\pi+\theta)=-\sin\theta`

`\sin(5\pi)/(4)=-(1)/(√(2))`

`\cos\theta =\cos((5\pi)/(4)`

`\cos\theta =\cos(\pi+(\pi)/(4)`

`\cos\theta =-\cos((\pi)/(4)`
`\because \cos(\pi+\theta)=-\cos\theta`

`\cos(5\pi)/(4)=-(1)/(√(2))`

`\tan\theta =\tan((5\pi)/(4)`

`\tan\theta =\tan(\pi+(\pi)/(4)`

`\tan\theta =\tan((\pi)/(4)`
`\because \tan(\pi+\theta)=\tan\theta`

`\tan(5\pi)/(4)=1`

Answer 2

`sin( (5 \pi )/(4)) = 0.07` rounded to two decimal places

If you have a scientific calculator, you can work this out by first change the setting from degree to radian


`cos( (5 \pi )/(4)) = 0.998` rounded to three decimal places


`tan( (5 \pi )/(4)) = 0.069` rounded to three decimal places