If -is in the first quadrant- then -1 - sin 2- - cos- True-False-

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Complementary Trigonometric ratios

If θ is in th...

Question

If $θ$ is in the first quadrant, then $\sqrt{(1 - s i n 2 θ)}$ = - cos $θ$

True

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False

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Solution

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\cos θ = \frac{8}{17}

\cos (\frac{π}{6} + θ) + \cos (\frac{π}{4} - θ) + \cos (\frac{2 π}{3} - θ) = (\frac{\sqrt{3} - 1}{2} + \frac{1}{\sqrt{2}}) \frac{23}{17}

θ

c o s θ = \frac{8}{17},

c o s (\frac{π}{6} + θ) + c o s (\frac{π}{4} - θ) + c o s (\frac{2 π}{3} - θ)

= (\frac{\sqrt{3} - 1}{2} + \frac{1}{\sqrt{2}}) \frac{23}{17}

If $θ$ is in the first quadrant, then $\sqrt{(1 - s i n 2 θ)}$ = - cos $θ$

tan θ = \frac{1}{\sqrt{5}}

θ

cos θ

θ = \frac{1}{\sqrt{5}}

θ

cos θ

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