11 Section 2.3 The Sine and Cosine Functions
- Find the exact value of each part below.
a. [latex]\sin (\frac{13\pi}{4})[/latex]
b. [latex]\sin (-\frac{7\pi}{6})[/latex]
c. [latex]\cos (\frac{14\pi}{3})[/latex]
d. [latex]\sin (\frac{15\pi}{4})[/latex]
e. [latex]\cos (\frac{13\pi}{3})[/latex]
f. [latex]\cos(-\frac{5\pi}{6})[/latex]
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Answers
a. [latex]-\frac{\sqrt{2}}{2}[/latex]
b. [latex]\frac{1}{2}[/latex]
c. [latex]-\frac{1}{2}[/latex]
d. [latex]-\frac{\sqrt{2}}{2}[/latex]
e. [latex]\frac{1}{2}[/latex]
f. [latex]-\frac{\sqrt{3}}{2}[/latex].
2. Find four different values for:
a. [latex]t[/latex] for [latex]\sin (t)=-\frac{1}{2}[/latex].
b. [latex]t[/latex] for [latex]\cos (t)=\frac{\sqrt{3}}{2}[/latex]
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Answers
a. While there are infinite answers to this, here are some examples:
[latex]-\frac{5\pi}{6}, -\frac{\pi}{6}, \frac{7\pi}{6}, \frac{11\pi}{6}, \frac{19\pi}{6}, \frac{23\pi}{6}...[/latex]
b. While there are infinite answers to this, here are some examples:
[latex]-\frac{\pi}{6}, -\frac{11\pi}{6}, \frac{\pi}{6}, \frac{11\pi}{6}, \frac{13\pi}{6}, \frac{23\pi}{6} ...[/latex]