- Demonstrate the ability to evaluate an inverse sine function
- Demonstrate the ability to evaluate an inverse cosine function
- Demonstrate the ability to evaluate an inverse tangent function
- Demonstrate the ability to evaluate an inverse secant function
- Demonstrate the ability to evaluate an inverse cosecant function
- Demonstrate the ability to evaluate an inverse cotangent function
#1:
Instructions: Find the exact value.
$$a)\hspace{.1em}\text{sin}^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$
$$b)\hspace{.1em}\text{tan}^{-1}\left(0\right)$$
$$c)\hspace{.1em}\text{sec}^{-1}\left(-2\right)$$
$$d)\hspace{.1em}\text{cot}^{-1}\left(-1\right)$$
$$e)\hspace{.1em}\text{cot}^{-1}\left(\sqrt{3}\right)$$
$$f)\hspace{.1em}\text{csc}^{-1}\left(-\sqrt{2}\right)$$
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#2:
Instructions: Find the exact value.
$$a)\hspace{.1em}\text{sin}^{-1}\left(\text{sin}\frac{3π}{4}\right)$$
$$b)\hspace{.1em}\text{cos}^{-1}\left(\text{cos}\frac{2π}{3}\right)$$
$$c)\hspace{.1em}\text{tan}^{-1}\left(\text{tan}\frac{11π}{6}\right)$$
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#3:
Instructions: Find the exact value.
$$a)\hspace{.1em}\text{csc}\left(\text{sin}^{-1}\left(\frac{12}{13}\right)\right)$$
$$b)\hspace{.1em}\text{tan}\left(\text{cos}^{-1}\left(\frac{3}{5}\right)\right)$$
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#4:
Instructions: Find the exact value.
$$a)\hspace{.1em}\text{cot}\left(\text{sin}^{-1}\left(\frac{3}{4}\right)\right)$$
Instructions: Write as an algebraic expression in u.
$$b)\hspace{.1em}\text{sec}\left(\text{sin}^{-1}\left(\frac{u}{\sqrt{u^2 + 4}}\right)\right)$$
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#5:
Instructions: Find the exact value.
$$a)\hspace{.1em}\text{cos}\left(\text{tan}^{-1}\left(\frac{5}{12}\right) - \text{tan}^{-1}\left(\frac{3}{4}\right)\right)$$
$$b)\hspace{.1em}\text{tan}\left(2\text{sin}^{-1}\left(\frac{2}{5}\right)\right)$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}{-}\frac{π}{3}$$
$$b)\hspace{.1em}0$$
$$c)\hspace{.1em}\frac{2π}{3}$$
$$d)\hspace{.1em}\frac{3π}{4}$$
$$e)\hspace{.1em}\frac{π}{6}$$
$$f)\hspace{.1em}{-}\frac{π}{4}$$
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#2:
Solutions:
$$a)\hspace{.1em}\frac{π}{4}$$
$$b)\hspace{.1em}\frac{2π}{3}$$
$$c)\hspace{.1em}{-}\frac{π}{6}$$
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#3:
Solutions:
$$a)\hspace{.1em}\frac{13}{12}$$
$$b)\hspace{.1em}\frac{4}{3}$$
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#4:
Solutions:
$$a)\hspace{.1em}\frac{\sqrt{7}}{3}$$
$$b)\hspace{.1em}\frac{\sqrt{u^2 + 4}}{2}$$ $$-\frac{π}{2}< θ < \frac{π}{2}$$ 
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#5:
Solutions:
$$a)\hspace{.1em}\frac{63}{65}$$
$$b)\hspace{.1em}\frac{4 \sqrt{21}}{17}$$
