1. Find the angle of smallest positive measure coterminal with an angle of the given measure:
a. 520
b. - 75
2. Points A (1,0) and B (.6,-.8) are points on a unit circle O. If the measure of angle AOB = 0 {w/ a line in the middle}
Find
a. sin 0
b. cos 0
c. tan 0
To find the angle of smallest positive measure coterminal with a given angle, you can use the concept of coterminal angles. Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 360 degrees (or 2π radians).
1. a. To find the angle of smallest positive measure coterminal with 520 degrees, subtract or add multiples of 360 degrees until you get an angle between 0 and 360 degrees. In this case, subtracting 360 degrees once from 520 degrees will give you the angle of smallest positive measure coterminal with 520 degrees:
520 degrees - 360 degrees = 160 degrees
Therefore, the angle of smallest positive measure coterminal with 520 degrees is 160 degrees.
1. b. To find the angle of smallest positive measure coterminal with -75 degrees, add multiples of 360 degrees until you get an angle between 0 and 360 degrees. In this case, adding 360 degrees once to -75 degrees will give you the angle of smallest positive measure coterminal with -75 degrees:
-75 degrees + 360 degrees = 285 degrees
Therefore, the angle of smallest positive measure coterminal with -75 degrees is 285 degrees.
2. To find the values of sin 0, cos 0, and tan 0 for angle AOB = 0 degrees on a unit circle, you can use the coordinates of points A(1,0) and B(0.6,-0.8) on the unit circle.
a. sin 0 represents the y-coordinate of the point on the unit circle corresponding to angle AOB = 0 degrees. Since angle AOB = 0 degrees is on the x-axis, the y-coordinate of the point is 0.
Therefore, sin 0 = 0.
b. cos 0 represents the x-coordinate of the point on the unit circle corresponding to angle AOB = 0 degrees. The x-coordinate of point A(1,0) is 1.
Therefore, cos 0 = 1.
c. tan 0 represents the ratio of sin 0 to cos 0. Since sin 0 = 0 and cos 0 = 1, the value of tan 0 is 0 divided by 1, which is 0.
Therefore, tan 0 = 0.