5.2 Unit Circle: Sine and Cosine Functions
5.1 Section Exercises
Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.
Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.
1320 rad 210.085 RPM
7 in./s, 4.77 RPM, 28.65 deg/s
794 miles per hour
2,234 miles per hour
5.2 Section Exercises
The unit circle is a circle of radius 1 centered at the origin.
Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle, formed by the terminal side of the angle and the horizontal axis.
The sine values are equal.
37.5 seconds, 97.5 seconds, 157.5 seconds, 217.5 seconds, 277.5 seconds, 337.5 seconds
5.3 Section Exercises
Yes, when the reference angle is and the terminal side of the angle is in quadrants I and III. Thus, at the sine and cosine values are equal.
Substitute the sine of the angle in for in the Pythagorean Theorem Solve for and take the negative solution.
The outputs of tangent and cotangent will repeat every units.
If , , , ,
, , ,
, , , ,
13.77 hours, period:
5.4 Section Exercises
The tangent of an angle is the ratio of the opposite side to the adjacent side.
For example, the sine of an angle is equal to the cosine of its complement; the cosine of an angle is equal to the sine of its complement.
1036.73 miles per hour
sine, cosecant, tangent, cotangent