- Demonstrate the ability to solve trigonometric equations using square roots
- Demonstrate the ability to solve trigonometric equations using squaring
- Demonstrate the ability to solve trigonometric equations using identities
#1:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}{-}\text{cos}^2 θ=3 - 5 \text{cos}^2 θ$$
$$b)\hspace{.1em}1 + 3\text{tan}^2 θ=4 \text{tan}^2 θ$$
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#2:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}7=4\text{sin}^2 θ + 4$$
$$b)\hspace{.1em}{-}2=\text{cot}^2 θ - 3$$
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#3:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}\text{sec}\hspace{.1em}θ + 1=\text{tan}^2 θ$$
$$b)\hspace{.1em}2 + \text{sin}^2 θ=\text{cos}^2 θ + 3\text{sin}\hspace{.1em}θ$$
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#4:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}\text{cot}^2 θ - 3\text{csc}\hspace{.1em}θ + 3=0$$
$$b)\hspace{.1em}3\text{sin}^2 θ + 2=\text{cos}^2 θ - 4 \text{sin}\hspace{.1em}θ$$
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#5:
Instructions: Solve each equation for 0 ≤ θ < 2π.
$$a)\hspace{.1em}1 + \text{sec}\hspace{.1em}θ - 2 \text{tan}\hspace{.1em}θ={-}\text{tan}\hspace{.1em}θ$$
$$b)\hspace{.1em}{-}\text{csc}\hspace{.1em}θ + 1=\text{cot}\hspace{.1em}θ + 2$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}\left\{\frac{π}{6}, \frac{5π}{6}, \frac{7π}{6}, \frac{11π}{6}\right\}$$
$$b)\hspace{.1em}\left\{\frac{π}{4}, \frac{3π}{4}, \frac{5π}{4}, \frac{7π}{4}\right\}$$
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#2:
Solutions:
$$a)\hspace{.1em}\left\{\frac{π}{3}, \frac{2π}{3}, \frac{4π}{3}, \frac{5π}{3}\right\}$$
$$b)\hspace{.1em}\left\{\frac{π}{4}, \frac{3π}{4}, \frac{5π}{4}, \frac{7π}{4}\right\}$$
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#3:
Solutions:
$$a)\hspace{.1em}\left\{\frac{π}{3}, π, \frac{5π}{3}\right\}$$
$$b)\hspace{.1em}\left\{\frac{π}{6}, \frac{π}{2}, \frac{5π}{6}\right\}$$
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#4:
Solutions:
$$a)\hspace{.1em}\left\{\frac{π}{6}, \frac{π}{2}, \frac{5π}{6}\right\}$$
$$b)\hspace{.1em}\left\{\frac{7π}{6}, \frac{11π}{6}\right\}$$
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#5:
Solutions:
$$a)\hspace{.1em}\{π\}$$
$$b)\hspace{.1em}\left\{\frac{3π}{2}\right\}$$
