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10-168.

Without a calculator, what are two solutions to each of the following equations for $0^\circ ≤ θ < 360^\circ$ ?

$\text{cos}(θ) =\frac { 1 } { 2 }$
Answer (a):
Draw a unit circle.
$\text{The cosine is where the }x\text{-value (red line) is }\frac{1}{2}.$
Answers: $60^\circ$ and $300^\circ$

$\text{tan}\left(θ\right) = -1$
Answer (b):
$135^\circ$ and $315^\circ$

$\text{sin}(θ) =\frac { \sqrt { 3 } } { 2 }$
Hint (c):
Draw and label a unit circle as in part (a). Don't forget that the sine is the $y$ -value! Which quadrants will the angles be in?

$\text{cos}(θ) = -\frac { \sqrt { 3 } } { 2 }$
Hint (d):
See part (c).

Compute without a calculator

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