The measure 0 of an angle in standard position is given. Find the exact values of cos 0 and sin 0 for the angle measure.
7π/3 radians
To find the exact values of cos(0) and sin(0), we use the angle measure of 7π/3 radians.
cos(0) is the x-coordinate of the point on the unit circle corresponding to the angle measurement 7π/3 radians.
sin(0) is the y-coordinate of the point on the unit circle corresponding to the angle measurement 7π/3 radians.
To find these coordinates, we can convert 7π/3 radians to degrees as follows:
7π/3 radians = (7π/3) * (180/π) = 7 * 60 = 420 degrees
Now, the point on the unit circle corresponding to the angle measurement 420 degrees is the same as the point corresponding to the angle measurement -60 degrees (since angles that differ by integer multiples of 360 degrees are coterminal).
To determine the coordinates of this point, recall that the unit circle is defined as a circle centered at the origin with a radius of 1. The x-coordinate of a point on the unit circle can be found using the cosine function, and the y-coordinate can be found using the sine function.
cos(-60 degrees) = cos(60 degrees) = 1/2
sin(-60 degrees) = sin(60 degrees) = √3/2
Therefore, the exact values of cos(0) and sin(0) for the angle measure 7π/3 radians are:
cos(0) = 1/2
sin(0) = √3/2