- Demonstrate the ability to solve basic trigonometric equations
- Demonstrate the ability to solve trigonometric equations using factoring
#1:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}{-}4\text{sec}\hspace{.1em}θ + 4 + 2\text{sec}^2 θ=\text{sec}^2 θ$$
$$b)\hspace{.1em}\sqrt{2}\text{sin}\hspace{.1em}θ\text{cos}\hspace{.1em}θ + 3\text{cos}\hspace{.1em}θ=4\text{cos}\hspace{.1em}θ$$
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#2:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}3\text{cos}\hspace{.1em}θ=1 + 2\text{cos}^2 θ$$
$$b)\hspace{.1em}1 + 3\text{cos}^2 θ + 3 \text{cos}\hspace{.1em}θ=\text{cos}^2 θ$$
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#3:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}3\text{csc}\hspace{.1em}θ=\sqrt{3}\text{csc}\hspace{.1em}θ \text{tan}\hspace{.1em}θ + 2 \text{csc}\hspace{.1em}θ$$
$$b)\hspace{.1em}{-}\sqrt{3}\text{sec}\hspace{.1em}θ \text{tan}\hspace{.1em}θ + 4\text{sec}\hspace{.1em}θ=3\text{sec}\hspace{.1em}θ$$
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#4:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}{-}1 - 2\text{cot}^2 θ=-\text{cot}^2 θ + 2 \text{cot}\hspace{.1em}θ$$
$$b)\hspace{.1em}{-}\sqrt{3}\text{cot}\hspace{.1em}θ + 2 \text{cot}\hspace{.1em}θ\text{sin}\hspace{.1em}θ - 3\text{sin}\hspace{.1em}θ=-3\text{sin}\hspace{.1em}θ$$
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#5:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}{-}2=-\text{sec}^2 θ - \text{sec}\hspace{.1em}θ$$
$$b)\hspace{.1em}\sqrt{3}\text{sec}\hspace{.1em}θ + 3 \text{sec}\hspace{.1em}θ \text{cot}\hspace{.1em}θ=0$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}\left\{\frac{π}{3}, \frac{5π}{3}\right\}$$
$$b)\hspace{.1em}\left\{\frac{π}{4}, \frac{π}{2}, \frac{3π}{4}, \frac{3π}{2}\right\}$$
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#2:
Solutions:
$$a)\hspace{.1em}\left\{0, \frac{π}{3}, \frac{5π}{3}\right\}$$
$$b)\hspace{.1em}\left\{\frac{2π}{3}, π, \frac{4π}{3}\right\}$$
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#3:
Solutions:
$$a)\hspace{.1em}\left\{\frac{π}{6}, \frac{7π}{6}\right\}$$
$$b)\hspace{.1em}\left\{\frac{π}{6}, \frac{7π}{6}\right\}$$
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#4:
Solutions:
$$a)\hspace{.1em}\left\{\frac{3π}{4}, \frac{7π}{4}\right\}$$
$$b)\hspace{.1em}\left\{\frac{π}{3}, \frac{π}{2}, \frac{2π}{3}, \frac{3π}{2}\right\}$$
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#5:
Solutions:
$$a)\hspace{.1em}\left\{0, \frac{2π}{3}, \frac{4π}{3}\right\}$$
$$b)\hspace{.1em}\left\{\frac{2π}{3}, \frac{5π}{3}\right\}$$