How do you find the sine, cosine, and tangent of 19pi/2 radians?

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How do you find the sine, cosine, and tangent of 19pi/2 radians?

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Answer 1 · 2015-11-05T05:12:18

$sin (\frac{3 π}{2}) = - 1$ $sin((3pi)/2) = -1$
$cos (\frac{3 π}{2}) = 0$ $cos((3pi)/2) = 0$
$tan (\frac{3 π}{2}) =$ $tan((3pi)/2) =$ infinity/undefined

Explanation:

If we take away $2 π$ $2pi$ radians from the angle, it will still be the same angle. So, we do that until it is a more recognizable angle. Since $\frac{4 π}{2}$ $(4pi)/2$ is the same as $2 π$ $2pi$ , we will use that.

$\frac{19 π}{2} - \frac{4 π}{2} - \frac{4 π}{2} - \frac{4 π}{2} - \frac{4 π}{2} = \frac{3 π}{2}$ $(19pi)/2 - (4pi)/2 - (4pi)/2 - (4pi)/2 - (4pi)/2 = (3pi)/2$
Now to find the sin, cos, and tan values of $\frac{3 π}{2}$ $(3pi)/2$ , use the unit circle.

$sin (\frac{3 π}{2}) = - 1$ $sin((3pi)/2) = -1$
$cos (\frac{3 π}{2}) = 0$ $cos((3pi)/2) = 0$
$tan (\frac{3 π}{2}) =$ $tan((3pi)/2) =$ infinity/undefined
![https://en.wikipedia.org/wiki/Unit_circle]( useruploads.socratic.org )

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How do you find the sine, cosine, and tangent of 19pi/2 radians?

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