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. Show your all your work
7π/4
To find the values of cos(0) and sin(0) for an angle in standard position, we can use the unit circle.
The angle measure 7π/4 is in the fourth quadrant of the unit circle.
To find cos(7π/4), we look at the x-coordinate of the point on the unit circle that corresponds to 7π/4.
In the fourth quadrant, the x-coordinate is negative and its absolute value is the cosine value.
Since the angle 7π/4 is halfway between π and 2π, we know that cos(7π/4) is the same as cos(π/4) which is equal to √2/2.
Therefore, cos(7π/4) = √2/2.
To find sin(7π/4), we look at the y-coordinate of the point on the unit circle that corresponds to 7π/4.
In the fourth quadrant, the y-coordinate is negative and its absolute value is the sine value.
Since the angle 7π/4 is halfway between π and 2π, we know that sin(7π/4) is the same as sin(π/4) which is equal to √2/2.
Therefore, sin(7π/4) = -√2/2.
So the exact values of cos(0) and sin(0) for the angle 7π/4 are √2/2 and -√2/2, respectively.