Answer: See Below
Step-by-step explanation:
NOTE: You need the Unit Circle to answer these (attached)
5) cos (t) = 1
Where on the Unit Circle does cos = 1?
Answer: at 0π (0°) and all rotations of 2π (360°)
In radians: t = 0π + 2πn
In degrees: t = 0° + 360n
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[tex]6)\quad sin (t) = \dfrac{1}{2}[/tex]
Where on the Unit Circle does [tex]sin = \dfrac{1}{2}[/tex]
Hint: sin is only positive in Quadrants I and II
[tex]\text{Answer: at}\ \dfrac{\pi}{6}\ (30^o)\ \text{and at}\ \dfrac{5\pi}{6}\ (150^o)\ \text{and all rotations of}\ 2\pi \ (360^o)[/tex]
[tex]\text{In radians:}\ t = \dfrac{\pi}{6} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{6} + 2\pi n[/tex]
In degrees: t = 30° + 360n and 150° + 360n
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[tex]7)\quad tan (t) = -\sqrt3[/tex]
Where on the Unit Circle does [tex]\dfrac{sin}{cos} = \dfrac{-\sqrt3}{1}\ or\ \dfrac{\sqrt3}{-1}\quad \rightarrow \quad (1,-\sqrt3)\ or\ (-1, \sqrt3)[/tex]
Hint: sin and cos are only opposite signs in Quadrants II and IV
[tex]\text{Answer: at}\ \dfrac{2\pi}{3}\ (120^o)\ \text{and at}\ \dfrac{5\pi}{3}\ (300^o)\ \text{and all rotations of}\ 2\pi \ (360^o)[/tex]
[tex]\text{In radians:}\ t = \dfrac{2\pi}{3} + 2\pi n \quad \text{and}\quad \dfrac{5\pi}{3} + 2\pi n[/tex]
In degrees: t = 120° + 360n and 300° + 360n
