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How do you evaluate sin(-3π/2)?

1 Answer

Dec 17, 2015

$sin (- \frac{3 π}{2}) = 1$ $sin(-(3pi)/2) = 1$

Explanation:

As an angle $- \frac{3 π}{2}$ $-(3pi)/2$ is equivalent to $\frac{π}{2}$ $pi/2$

$- \frac{3 π}{2}$ $-(3pi)/2$ is $\frac{3}{4}$ $3/4$ of a circle in a clockwise direction.
$\frac{π}{2}$ $pi/2$ is $\frac{1}{4}$ $1/4$ of a circle in a counter clockwise direction.

$sin (\frac{π}{2}) = 1$ $sin(pi/2) =1$

If you think in terms of a unit radius circular segment centered on the origin of the Cartesian plane with its base along the positive X-axis, then the inscribed right-angled triangle at $\frac{π}{2}$ $pi/2$ will have a vertex on the positive Y-axis and both the hypotenuse and opposite side will have a length of $1$ $1$

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