Question

The measure of angle θ is 7pi/4 . The measure of its reference angle is *Blank* °, and tan θ is *blank*

Answer 1

Since the measure of angle
`\Theta` is
`(7\Pi )/(4)`

The measure of its reference angle =
`(7* 180^(\circ))/(4)`

=
`=315^(\circ)`

Now we have to compute the value of
`\tan \Theta`

`\tan \Theta = \tan (7\Pi )/(4)`

`= \tan (2\Pi -(\Pi )/(4))`

The value of (
`(2\Pi -(\Pi )/(4))`) lies in the fourth quadrant. In fourth quadrant, the value of tan is always negative.

So,
`\tan (2\Pi -(\Pi )/(4))`

`= -\tan ((\Pi )/(4))`

= -1.