Answer: (a) IV (b) negative (c) [tex]\frac{\pi}{3}[/tex] (d) A (e) [tex]-\sqrt{3}[/tex]
Step-by-step explanation:
a) [tex]-\frac{7\pi}{3}[/tex] + [tex]\frac{6\pi}{3}[/tex] = [tex]-\frac{\pi}{3}[/tex]
[tex]-\frac{\pi}{3}[/tex] + [tex]\frac{6\pi}{3}[/tex] = [tex]\frac{5\pi}{3}[/tex] which is located in Quadrant IV on the Unit Circle
b) tan is [tex]\frac{sin}{cos}[/tex]. In Quadrant IV, sin is negative and cos is positive so their quotient is negative.
c) the reference angle is the angle from [tex]\frac{5\pi}{3}[/tex] to 2π which is [tex]\frac{\pi}{3}[/tex].
d) Since Quadrant IV is below the x-axis, then another angle would be negative of the reference angle = -tan[tex](\frac{\pi}{3})[/tex]
e) tan is [tex]\frac{sin}{cos}[/tex]. tan [tex](\frac{5\pi}{3})[/tex] = [tex]-\frac{\sqrt{3}}{2}[/tex] ÷ [tex]\frac{1}{2}[/tex] = [tex]-\sqrt{3}[/tex]
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Answer: C
Step-by-step explanation:
[tex]\frac{\pi}{4}[/tex] has a reference angle of [tex]\frac{\pi}{4}[/tex]. All of the angles on the Unit Circle that have a reference angle of [tex]\frac{\pi}{4}[/tex] are: [tex]\frac{3\pi}{4}[/tex], [tex]\frac{5\pi}{4}[/tex], and [tex]\frac{7\pi}{4}[/tex].
option A is included above. option B reduces to [tex]\frac{\pi}{4}[/tex], which is included above. option D reduces to [tex]\frac{3\pi}{4}[/tex], which is included above. option C is not included in the family of angles given above.
