- Demonstrate the ability to find trigonometric function values given on value and the quadrant
#1:
Instructions: Find the values of the five trigonometric functions not given.
$$a)\hspace{.1em}\text{tan}\hspace{.2em}θ=\frac{2}{3}, \text{sin}\hspace{.2em}θ < 0$$
$$b)\hspace{.1em}\text{sec}\hspace{.2em}θ=-\frac{\sqrt{5}}{2}, \text{sin}\hspace{.2em}θ > 0$$
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#2:
Instructions: Find the values of the five trigonometric functions not given.
$$a)\hspace{.1em}\text{tan}\hspace{.2em}θ=-\frac{2\sqrt{5}}{5}, \text{sin}\hspace{.2em}θ < 0$$
$$b)\hspace{.1em}\text{csc}\hspace{.2em}θ=\frac{\sqrt{17}}{4}, \text{cos}\hspace{.2em}θ > 0$$
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#3:
Instructions: Find the values of the five trigonometric functions not given.
$$a)\hspace{.1em}\text{cot}\hspace{.2em}θ=-\frac{4}{3}, \text{cos}\hspace{.2em}θ < 0$$
$$b)\hspace{.1em}\text{tan}\hspace{.2em}θ=-\frac{2}{3}, \text{cos}\hspace{.2em}θ > 0$$
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#4:
Instructions: Find the values of the five trigonometric functions not given.
$$a)\hspace{.1em}\text{sec}\hspace{.2em}θ=\frac{5}{4}, \text{sin}\hspace{.2em}θ < 0$$
$$b)\hspace{.1em}\text{sec}\hspace{.2em}θ=\frac{5}{4}, \text{sin}\hspace{.2em}θ > 0$$
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#5:
Instructions: Find the values of the five trigonometric functions not given.
$$a)\hspace{.1em}\text{csc}\hspace{.2em}θ=-\frac{13}{12}, \text{cos}\hspace{.2em}θ > 0$$
$$b) \hspace{.1em}\text{sec}\hspace{.2em}θ=\frac{17}{15}, \text{sin}\hspace{.2em}θ < 0$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{2\sqrt{13}}{13}$$ $$\text{cos}\hspace{.2em}θ=-\frac{3\sqrt{13}}{13}$$ $$\text{csc}\hspace{.2em}θ=-\frac{\sqrt{13}}{2}$$ $$\text{sec}\hspace{.2em}θ=-\frac{\sqrt{13}}{3}$$ $$\text{cot}\hspace{.2em}θ=\frac{3}{2}$$
$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{\sqrt{5}}{5}$$ $$\text{cos}\hspace{.2em}θ=-\frac{2\sqrt{5}}{5}$$ $$\text{tan}\hspace{.2em}θ=-\frac{1}{2}$$ $$\text{csc}\hspace{.2em}θ=\sqrt{5}$$ $$\text{cot}\hspace{.2em}θ=-2$$
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#2:
Solutions:
$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{2}{3}$$ $$\text{cos}\hspace{.2em}θ=\frac{\sqrt{5}}{3}$$ $$\text{csc}\hspace{.2em}θ=-\frac{3}{2}$$ $$\text{sec}\hspace{.2em}θ=\frac{3\sqrt{5}}{5}$$ $$\text{cot}\hspace{.2em}θ=-\frac{\sqrt{5}}{2}$$
$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{4\sqrt{17}}{17}$$ $$\text{cos}\hspace{.2em}θ=\frac{\sqrt{17}}{17}$$ $$\text{tan}\hspace{.2em}θ=4$$ $$\text{sec}\hspace{.2em}θ=\sqrt{17}$$ $$\text{cot}\hspace{.2em}θ=\frac{1}{4}$$
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#3:
Solutions:
$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{3}{5}$$ $$\text{cos}\hspace{.2em}θ=-\frac{4}{5}$$ $$\text{tan}\hspace{.2em}θ=-\frac{3}{4}$$ $$\text{csc}\hspace{.2em}θ=\frac{5}{3}$$ $$\text{sec}\hspace{.2em}θ=-\frac{5}{4}$$
$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{2\sqrt{13}}{13}$$ $$\text{cos}\hspace{.2em}θ=\frac{3\sqrt{13}}{13}$$ $$\text{csc}\hspace{.2em}θ=-\frac{\sqrt{13}}{2}$$ $$\text{sec}\hspace{.2em}θ=\frac{\sqrt{13}}{3}$$ $$\text{cot}\hspace{.2em}θ=-\frac{3}{2}$$
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#4:
Solutions:
$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{3}{5}$$ $$\text{cos}\hspace{.2em}θ=\frac{4}{5}$$ $$\text{tan}\hspace{.2em}θ=-\frac{3}{4}$$ $$\text{csc}\hspace{.2em}θ=-\frac{5}{3}$$ $$\text{cot}\hspace{.2em}θ=-\frac{4}{3}$$
$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{3}{5}$$ $$\text{cos}\hspace{.2em}θ=\frac{4}{5}$$ $$\text{tan}\hspace{.2em}θ=\frac{3}{4}$$ $$\text{csc}\hspace{.2em}θ=\frac{5}{3}$$ $$\text{cot}\hspace{.2em}θ=\frac{4}{3}$$
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#5:
Solutions:
$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{12}{13}$$ $$\text{cos}\hspace{.2em}θ=\frac{5}{13}$$ $$\text{tan}\hspace{.2em}θ=-\frac{12}{5}$$ $$\text{sec}\hspace{.2em}θ=\frac{13}{5}$$ $$\text{cot}\hspace{.2em}θ=-\frac{5}{12}$$
$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{8}{17}$$ $$\text{cos}\hspace{.2em}θ=\frac{15}{17}$$ $$\text{tan}\hspace{.2em}θ=-\frac{8}{15}$$ $$\text{csc}\hspace{.2em}θ=-\frac{17}{8}$$ $$\text{cot}\hspace{.2em}θ=-\frac{15}{8}$$
