Question

HELP WITH THESE QUESTIONS PART 2..

Answer 1

Answer: (a) IV (b) negative (c) $\frac{\pi}{3}$ (d) A (e) $-\sqrt{3}$

Step-by-step explanation:

a) $-\frac{7\pi}{3}$ + $\frac{6\pi}{3}$ = $-\frac{\pi}{3}$

$-\frac{\pi}{3}$ + $\frac{6\pi}{3}$ = $\frac{5\pi}{3}$ which is located in Quadrant IV on the Unit Circle

b) tan is $\frac{sin}{cos}$.  In Quadrant IV, sin is negative and cos is positive so their quotient is negative.

c) the reference angle is the angle from $\frac{5\pi}{3}$ to 2π which is $\frac{\pi}{3}$.

d) Since Quadrant IV is below the x-axis, then another angle would be negative of the reference angle = -tan$(\frac{\pi}{3})$

e) tan is $\frac{sin}{cos}$. tan $(\frac{5\pi}{3})$ = $-\frac{\sqrt{3}}{2}$ ÷ $\frac{1}{2}$ = $-\sqrt{3}$

************************************************************

Answer: C

Step-by-step explanation:

$\frac{\pi}{4}$ has a reference angle of $\frac{\pi}{4}$.  All of the angles on the Unit Circle that have a reference angle of $\frac{\pi}{4}$ are: $\frac{3\pi}{4}$, $\frac{5\pi}{4}$, and $\frac{7\pi}{4}$.

option A is included above.  option B reduces to $\frac{\pi}{4}$, which is included above. option D reduces to $\frac{3\pi}{4}$, which is included above.  option C is not included in the family of angles given above.