**Radians**

**radian**is a way to measure angles based on how many radiuses lie along the arc intercepted by the central angle. For an angle in radians, where S = arc length:

Since there are pi radians in half a circle, and also 180 degrees in half a circle, you can convert degrees to radians and vice versa with the following proportion:

Also, we are expected to be able to work with revolutions. Recall that 1 revolution = 1 circumference = 360 degrees = 2pi radians.

Since rates are determined by the amount of change divided by time, the following formulas apply:

**The Unit Circle**

For any point on the unit circle, the *x* coordinate is the cosine of the central angle, and the *y* coordinate is the sine of the central angle. The following values should be memorized. Each point (*x, y*) indicates (*cos, sin*) of the central angle. (*diagram source*: The PreCal40S Blog)

**Graphs of Trig Functions**

Sine and Cosine graphs come in this format: ** y = a sin (bx) + c** where

*is the amplitude,*

**a***is the frequency (how many complete cycles in 2pi), and*

**b***is the vertical shift. The period, or the length of one cycle, can be obtained by .*

**c**For example, here is the graph of ** y = -3 cos (2x) + 4** from -2pi to 2pi, which has a period of pi:

**Practice Problems**

8. Write an equation for a sinusoidal graph with a minima at 0, a maxima at 4, and a period of pi.

9. What is the range of the function

**?**

*y*= -5cos*x*- 310. Find the linear speed in cm/sec and angular speed in radians/sec of a point on the edge of a rotating compact disk that makes 500 revolutions per minute. A standard cd is 12 cm in diameter.

(Solutions Pending)

(Solutions Pending)

## 1 comment:

Ms. Nowak where are the solutions??

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