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 $\frac{7\Pi }{4}$

The measure of its reference angle = $\frac{7\times 180^{\circ}}{4}$

=$=315^{\circ}$

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

$\tan \Theta = \tan \frac{7\Pi }{4}$

$= \tan (2\Pi -\frac{\Pi }{4})$

The value of ($(2\Pi -\frac{\Pi }{4})$) lies in the fourth quadrant. In fourth quadrant, the value of tan is always negative.

So, $\tan (2\Pi -\frac{\Pi }{4})$

$= -\tan (\frac{\Pi }{4})$

= -1.