- Demonstrate the ability to solve problems using the Reciprocal Identities
- Demonstrate the ability to solve problems using the Pythagorean Identities
- Demonstrate the ability to solve problems using the Quotient Identities
#1:
Instructions: Use identities to find the value of each expression.
a) Find cos θ and cot θ $$\text{csc}\hspace{.2em}θ=-5, \text{cos}\hspace{.2em}θ > 0$$
b) Find sin θ and cot θ $$\text{tan}\hspace{.2em}θ=-\frac{5}{6}, \text{csc}\hspace{.2em}θ > 0$$
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#2:
Instructions: Use identities to find the value of each expression.
a) Find cos θ and tan θ $$\text{sec}\hspace{.2em}θ=-\frac{6}{5}, \text{cot}\hspace{.2em}θ < 0$$
b) Find sin θ and cos θ $$\text{cot}\hspace{.2em}θ=\frac{7}{5}, \text{sec}\hspace{.2em}θ > 0$$
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#3:
Instructions: Use identities to find the value of each expression.
a) Find tan θ and cos θ $$\text{sin}\hspace{.2em}θ=\frac{1}{2}, \text{cot}\hspace{.2em}θ > 0$$
b) Find csc θ and sin θ $$\text{tan}\hspace{.2em}θ=\frac{1}{2}, \text{sec}\hspace{.2em}θ < 0$$
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#4:
Instructions: Use identities to find the value of each expression.
a) Find sec θ and csc θ $$\text{sin}\hspace{.2em}θ=\frac{2}{3}, \text{cot}\hspace{.2em}θ > 0$$
b) Find cos θ and sin θ $$\text{csc}\hspace{.2em}θ=-\frac{5}{3}, \text{tan}\hspace{.2em}θ < 0$$
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#5:
Instructions: Use identities to find the value of each expression.
a) Find sin θ and cos θ $$\text{sec}\hspace{.2em}θ=-\frac{7}{3}, \text{sin}\hspace{.2em}θ > 0$$
b) Find tan θ and cot θ $$\text{cos}\hspace{.2em}θ=-\frac{2}{5}, \text{csc}\hspace{.2em}θ > 0$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}\text{cos}\hspace{.2em}θ=\frac{2\sqrt{6}}{5}, \text{cot}\hspace{.2em}θ=-2\sqrt{6}$$
$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{5\sqrt{61}}{61}, \text{cot}\hspace{.2em}θ=-\frac{6}{5}$$
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#2:
Solutions:
$$a)\hspace{.1em}\text{cos}\hspace{.2em}θ=-\frac{5}{6}, \text{tan}\hspace{.2em}θ=-\frac{\sqrt{11}}{5}$$
$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{5\sqrt{74}}{74}, \text{cos}\hspace{.2em}θ=\frac{7\sqrt{74}}{74}$$
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#3:
Solutions:
$$a)\hspace{.1em}\text{tan}\hspace{.2em}θ=\frac{\sqrt{3}}{3}, \text{cos}\hspace{.2em}θ=\frac{\sqrt{3}}{2}$$
$$b)\hspace{.1em}\text{csc}\hspace{.2em}θ=-\sqrt{5}, \text{sin}\hspace{.2em}θ=-\frac{\sqrt{5}}{5}$$
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#4:
Solutions:
$$a)\hspace{.1em}\text{sec}\hspace{.2em}θ=\frac{3\sqrt{5}}{5}, \text{csc}\hspace{.2em}θ=\frac{3}{2}$$
$$b)\hspace{.1em}\text{cos}\hspace{.2em}θ=\frac{4}{5}, \text{sin}\hspace{.2em}θ=-\frac{3}{5}$$
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#5:
Solutions:
$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{2\sqrt{10}}{7}, \text{cos}\hspace{.2em}θ=-\frac{3}{7}$$
$$b)\hspace{.1em}\text{tan}\hspace{.2em}θ=-\frac{\sqrt{21}}{2}, \text{cot}\hspace{.2em}θ=-\frac{2\sqrt{21}}{21}$$
