- Demonstrate the ability to find the trigonometric function values of an acute angle
- Demonstrate the ability to write a function in terms of its cofunction
- Demonstrate the ability to solve equations using cofunction identities
#1:
Instructions: Find the six trigonometric functions for angle θ.
$$a)\hspace{.1em}$$
$$b)\hspace{.1em}$$
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#2:
Instructions: Find the six trigonometric functions for angle θ.
$$a)\hspace{.1em}$$
$$b)\hspace{.1em}$$
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#3:
Instructions: Write each function in terms of its cofunction.
$$a)\hspace{.1em}\text{cos}\hspace{.2em}51°$$
$$b)\hspace{.1em}\text{csc}\hspace{.2em}19°$$
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#4:
Instructions: Write each function in terms of its cofunction.
$$a)\hspace{.1em}\text{cot}\hspace{.2em}77°$$
$$b)\hspace{.1em}\text{sec}(θ + 15°)$$
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#5:
Instructions: Find one solution for each equation. Assume all angles are acute angles.
$$a)\hspace{.1em}\text{sin}(3θ - 6°)=\text{cos}(5θ-48°)$$
$$b) \hspace{.1em}\text{csc}(θ + 8°)=\text{sec}(3θ+10°)$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}$$ $$\text{sin}\hspace{.2em}θ=\frac{3}{5}$$ $$\text{cos}\hspace{.2em}θ=\frac{4}{5}$$ $$\text{tan}\hspace{.2em}θ=\frac{3}{4}$$ $$\text{csc}\hspace{.2em}θ=\frac{5}{3}$$ $$\text{sec}\hspace{.2em}θ=\frac{5}{4}$$ $$\text{cot}\hspace{.2em}θ=\frac{4}{3}$$
$$b)\hspace{.1em}$$ $$\text{sin}\hspace{.2em}θ=\frac{7}{25}$$ $$\text{cos}\hspace{.2em}θ=\frac{24}{25}$$ $$\text{tan}\hspace{.2em}θ=\frac{7}{24}$$ $$\text{csc}\hspace{.2em}θ=\frac{25}{7}$$ $$\text{sec}\hspace{.2em}θ=\frac{25}{24}$$ $$\text{cot}\hspace{.2em}θ=\frac{24}{7}$$
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#2:
Solutions:
$$a)\hspace{.1em}$$ $$\text{sin}\hspace{.2em}θ=\frac{4}{5}$$ $$\text{cos}\hspace{.2em}θ=\frac{3}{5}$$ $$\text{tan}\hspace{.2em}θ=\frac{4}{3}$$ $$\text{csc}\hspace{.2em}θ=\frac{5}{4}$$ $$\text{sec}\hspace{.2em}θ=\frac{5}{3}$$ $$\text{cot}\hspace{.2em}θ=\frac{3}{4}$$
$$b)\hspace{.1em}$$ $$\text{sin}\hspace{.2em}θ=\frac{2}{7}$$ $$\text{cos}\hspace{.2em}θ=\frac{3\sqrt{5}}{7}$$ $$\text{tan}\hspace{.2em}θ=\frac{2\sqrt{5}}{15}$$ $$\text{csc}\hspace{.2em}θ=\frac{7}{2}$$ $$\text{sec}\hspace{.2em}θ=\frac{7\sqrt{5}}{15}$$ $$\text{cot}\hspace{.2em}θ=\frac{3\sqrt{5}}{2}$$
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#3:
Solutions:
$$a)\hspace{.1em}\text{cos}\hspace{.2em}51°=\text{sin}\hspace{.2em}39°$$
$$b)\hspace{.1em}\text{csc}\hspace{.2em}19°=\text{sec}\hspace{.2em}71°$$
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#4:
Solutions:
$$a)\hspace{.1em}\text{cot}\hspace{.2em}77°=\text{tan}\hspace{.2em}13°$$
$$b)\hspace{.1em}\text{sec}(θ + 15°)=\text{csc}(75° - θ)$$
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#5:
Solutions:
$$a)\hspace{.1em}θ=18°$$
$$b)\hspace{.1em}θ=18°$$
