Question

What are the sine cosine and tangent of theta=7pi/4 radians

Answer 1

see explanation

Explanation:

`(7\pi )/(4)` is in the fourth quadrant

Where sin and tan are < 0 , cos > 0

The related acute angle is 2π -
`(7\pi )/(4)` =
`(\pi )/(4)`

Hence

sin([
`(7\pi )/(4)` ) = - sin(
`(\pi )/(4)`) = -
`(1)/(√(2) )` = -
`(√(2) )/(2)`

cos(
`(7\pi )/(4)`) = cos(
`(\pi )/(4)`) =
`(√(2) )/(2)`

tan(
`(7\pi )/(4)`= - tan(
`(\pi )/(4)` = - 1

Answer 2

`\sin\theta=-(1)/(√(2))`

`\cos\theta=(1)/(√(2))`

`\tan\theta=-1`.

Explanation:

We have to find the value of sine cosine and tangent of
`\theta=(7\pi)/(4)` radians.

`(7\pi)/(4)* (180)/(\pi)=315^(\circ)`

So,
`\theta=(7\pi)/(4)` lies in 4th quadrant. Sine and tangent are negative in 4th quadrant.

The value of sinθ is

`\sin\theta=\sin ((7\pi)/(4))`

`\sin\theta=\sin (2\pi-(\pi)/(4))`

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

`\sin\theta=-(1)/(√(2))`

The value of cosθ is

`\cos\theta=\cos ((7\pi)/(4))`

`\cos\theta=\cos (2\pi-(\pi)/(4))`

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

`\cos\theta=(1)/(√(2))`

The value of tanθ is

`\tan\theta=\tan ((7\pi)/(4))`

`\tan\theta=\tan (2\pi-(\pi)/(4))`

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

`\tan\theta=-1`

Therefore
`\sin\theta=-(1)/(√(2))`,
`\cos\theta=(1)/(√(2))` and
`\tan\theta=-1`.