SOLUTION: Find the exact value of tan theta if sec theta= 7/4

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Question 756209: Find the exact value of tan theta if sec theta= 7/4
Answer by lwsshak3(11628) About Me  (Show Source):
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Find the exact value of tan theta if sec theta= 7/4
tan%5E2%28x%29=sec%5E2%28x%29-1
tan%5E2%28x%29=%287%2F4%29%5E2-1
tan%5E2%28x%29=49%2F16-1
tan%5E2%28x%29=33%2F16
take sqrt of both sides
tan(x)=±√33/4
..
calculator check:
sec(x)=1/cos(x)=7/4
cos(x)=4/7
x≈55.15º, 304.85º
tan(x)=tan(55.15)≈1.4361..
exact value=√33/4≈1.4361..
or
tan(x)=tan(304.85º)≈-1.4361..
exact value=-√33/4≈-1.4361..