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Hitman42 [59]
3 years ago
14

Cos(−θ)=√3/3, sinθ<0

Mathematics
1 answer:
Delicious77 [7]3 years ago
7 0

Answer:

\sin\theta=-\frac{\sqrt{6}}{3}


Step-by-step explanation:

The given trigonometric equation is \cos(-\theta)=\frac{\sqrt{3} }{3}.

We can either use the Pythagorean identity or the right angle triangle  to solve for \sin\theta.

According to the Pythagorean identity,

\cos^2\theta+\sin^2\theta=1


Recall that, the cosine function is an even function, therefore

\cos(-\theta)=\cos(\theta)


\Rightarrow \cos(\theta)=\frac{\sqrt{3} }{3}.

We substitute this value in to the above Pythagorean identity to get;


(\frac{\sqrt{3}}{3})^2+\sin^2\theta=1


\Rightarrow \frac{3}{9}+\sin^2\theta=1


\Rightarrow \sin^2\theta=1-\frac{3}{9}


\Rightarrow \sin^2\theta=\frac{6}{9}


\Rightarrow \sin\theta=\pm \sqrt{\frac{6}{9}}


\Rightarrow \sin\theta=\pm \frac{\sqrt{6}}{3}


But we were given that,

\sin\theta\:, so we choose the negative value.

\Rightarrow \sin\theta=-\frac{\sqrt{6}}{3}


The correct answer is B







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