- Demonstrate the ability to find function values of an angle
#1:
Instructions: Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated.
$$a)\hspace{.1em}\text{sin}\hspace{.25em}θ, \hspace{.25em}\left(\sqrt{5}, 2\right)$$
$$b)\hspace{.1em}\text{csc}\hspace{.25em}θ, \hspace{.25em}\left(2, 2\sqrt{3}\right)$$
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#2:
Instructions: Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated.
$$a)\hspace{.1em}\text{sec}\hspace{.25em}θ, \hspace{.25em}\left(3, -\sqrt{7}\right)$$
$$b)\hspace{.1em}\text{cot}\hspace{.25em}θ, \hspace{.25em}\left(-\sqrt{15}, -7\right)$$
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#3:
Instructions: Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated.
$$a)\hspace{.1em}\text{cos}\hspace{.25em}θ, \hspace{.25em}\left(-6, -\sqrt{13}\right)$$
$$b)\hspace{.1em}\text{sec}\hspace{.25em}θ, \hspace{.25em}\left(-2\sqrt{5}, -4\right)$$
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#4:
Instructions: Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated.
$$a)\hspace{.1em}\text{sec}\hspace{.25em}θ, \hspace{.25em}\left(2\sqrt{3}, -2\right)$$
$$b)\hspace{.1em}\text{cos}\hspace{.25em}θ, \hspace{.25em}\left({-}\sqrt{13}, 6\right)$$
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#5:
Instructions: Find the trigonometric function values of angle θ if its terminal side is defined by the given ray.
$$a)\hspace{.1em}{-}6x - y=0, x ≤ 0$$
$$b) \hspace{.1em}{-}4x + 7y=0, x ≤ 0$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}\text{sin}\hspace{.25em}θ=\frac{2}{3}$$
$$b)\hspace{.1em}\text{csc}\hspace{.25em}θ=\frac{2\sqrt{3}}{3}$$
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#2:
Solutions:
$$a)\hspace{.1em}\text{sec}\hspace{.25em}θ=\frac{4}{3}$$
$$b)\hspace{.1em}\text{cot}\hspace{.25em}θ=\frac{\sqrt{15}}{7}$$
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#3:
Solutions:
$$a)\hspace{.1em}\text{cos}\hspace{.25em}θ={-}\frac{6}{7}$$
$$b)\hspace{.1em}\text{sec}\hspace{.25em}θ={-}\frac{3\sqrt{5}}{5}$$
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#4:
Solutions:
$$a)\hspace{.1em}\text{sec}\hspace{.25em}θ=\frac{2\sqrt{3}}{3}$$
$$b)\hspace{.1em}\text{cos}\hspace{.25em}θ={-}\frac{\sqrt{13}}{7}$$
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#5:
Solutions:
$$a)\hspace{.1em}\text{sin}\hspace{.25em}θ=\frac{6\sqrt{37}}{37}$$ $$\text{cos}\hspace{.25em}θ=-\frac{\sqrt{37}}{37}$$ $$\text{tan}\hspace{.25em}θ=-6$$ $$\text{csc}\hspace{.25em}θ=\frac{\sqrt{37}}{6}$$ $$\text{sec}\hspace{.25em}θ=-\sqrt{37}$$ $$\text{cot}\hspace{.25em}θ=-\frac{1}{6}$$
$$b)\hspace{.1em}\text{sin}\hspace{.25em}θ=-\frac{4\sqrt{65}}{65}$$ $$\text{cos}\hspace{.25em}θ=-\frac{7\sqrt{65}}{65}$$ $$\text{tan}\hspace{.25em}θ=\frac{4}{7}$$ $$\text{csc}\hspace{.25em}θ=-\frac{\sqrt{65}}{4}$$ $$\text{sec}\hspace{.25em}θ=-\frac{\sqrt{65}}{7}$$ $$\text{cot}\hspace{.25em}θ=\frac{7}{4}$$
