Question

In the xy-plane, the unit circle with center at the
origin O contains point A with coordinates (1,0)
and point B with coordinates
(3/4,4/5)
What is the
value of the sine of AOB ?

Answer 1

We want to find the sine of the angle AOB, we will get that the sine of that angle is equal to 0.73

Remember that the angle, measured counterclockwise from the positive x-axis, defined by a point (x, y) is given by:

θ = Arctan(y/x).

Where arctan(x) is the inverse tangent function.

Now, the angle between point A and point B is just the difference between the angles that define each:

$\theta_A = arctan(0/1) = 0\°\\\theta_B = arctan(\frac{4/5}{3/4} ) = 46.8\°$

Then the angle AOB is just:

AOB = 46.8° - 0° = 46.8°

Then the sine of that angle is:

sin(46.8°) = 0.73

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