Find the exact value of each of the following:

Warm-Up: January 30, 2014

4cot)

120tan)

135cos)6

5sin)

d

c

b

a

Homework Questions?

On Monday 8 minute time limit All or nothing Must be turned in by the end of 8 minutes

to count.

Trig Values Quiz

Graphs of Sine and Cosine Functions

Section 4.5Have out your graphs that you made.

(x, y) = (cos θ, sin θ) If we want a graph of sin θ, we can

plot y-values as a function of θ. ◦ You did this in the Making Waves activity

If we want a graph of cos θ, we can plot x-values as a function of θ.

Remember the Unit Circle

Cyclical (repeats) Continuous Goes through origin Has an amplitude of 1 Has a period of 2π Domain=ℝ (all real #s) Range = [-1, 1] Odd function

◦ Rotational symmetry

Sine Curve, y=sin θ

Amplitude = |A| = the half-height of the curve

Period = 2π/B◦The length of one cycle◦The horizontal distance between

consecutive corresponding points Phase Shift = C/B = distance the curve is

shifted right Vertical Shift = D = distance the curve is

shifted up

y = A sin(Bx-C) + D

Determine the amplitude, period, phase shift, and vertical shift of the function.

Warm-Up: January 31, 2014

463cos2 xy

Homework Questions?

Cyclical (repeats) Continuous y-intercept at (0, 1) Has an amplitude of 1 Has a period of 2π Domain=ℝ (all real numbers) Range = [-1, 1] Even function

◦ Symmetric across y-axis

Cosine Curve, y=cos θ

Amplitude = |A| = the half-height of the curve

Period = 2π/B◦The length of one cycle◦The horizontal distance between

consecutive corresponding points Phase Shift = C/B = distance the curve is

shifted right Vertical Shift = D = distance the curve is

shifted up

y = A cos(Bx-C) + D

Determine the amplitude, period, phase shift, and vertical shift of the function.

Example 1

342sin3 xy

Determine the amplitude, period, phase shift, and vertical shift of the function.

You-Try #1

1364sin5 xy

Determine the amplitude, period, phase shift, and vertical shift of the function. Then graph.

Example 2 82

3sin2

xy

Determine the amplitude, period, phase shift, and vertical shift of the function. Then graph.

You-Try #2 211

64sin7

xy

Page 493 #1-49 Every Other Odd Use graph paper for graphs Check graphs with your TI-83

Assignment

In Exercises 1-6, determine the amplitude of each function. Then graph the function and y=sin(x) in the same rectangular coordinate system for 0≤x≤2π.

In Exercises 7-16, determine the amplitude and period of each function. Then graph one period of the function.

First Four Problems

xyxy sin3)5sin4)1

xyxy 2sin3)132

1sin3)9