Question #39687

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Question #39687

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Answer 1 · 2017-07-02T07:22:24

$sin (θ) = \frac{4}{5}$ $sin(theta)=4/5$

Explanation:

Obtuse means that the angle is between 90˚ and 180˚.

$90 < (θ) < 180$ $90<(theta)<180$

We know the following is true for any angle $θ$ $theta$ , so substitute in the known information and solve for $sin (θ)$ $sin(theta)$ :

${cos}^{2} (θ) + {sin}^{2} (θ) = 1$ $cos^2(theta)+sin^2(theta)=1$

$\Rightarrow {sin}^{2} (θ) = 1 - {(- \frac{3}{5})}^{2} = 1 - \frac{9}{25} = \frac{25}{25} - \frac{9}{25} = \frac{16}{25}$ $rArrsin^2(theta)=1-(-3/5)^2=1-9/25=25/25-9/25=16/25$

Take the square root of both sides:

$\Rightarrow sin (θ) = \sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \pm \frac{4}{5}$ $rArrsin(theta)=sqrt(16/25)=sqrt(16)/sqrt(25)=+-4/5$

Now, is the answer the positive or negative square root? Well, you need to know the unit circle and it's symmetry properties. You will find that $sin (θ)$ $sin(theta)$ is positive in the first and second quadrants. An angle between 90˚ and 180˚ corresponds to the second quadrant. Therefore, the angle is the positive root.

$sin (θ) = \frac{4}{5}$ $sin(theta)=4/5$

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Question #39687

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