CHAPTER 4 – LESSON 1 How do you graph sine and cosine by unwrapping the unit circle?

Warm-Up/Activator Fill in the table (separate sheet) with the radian measure of the angles and then both the exact and approximate values for sine, cosine, and tangent of these angles.

Angle Chart for Unit Circle

Graphs of Functions Sine

Graphs of Functions Cosine

Graphs of Functions Tangent

Graphs of Functions Sine Cosine

Graphs of Functions Tan Cotangent

Graphs of Functions Secant Cosecant

Chapter 4 - Lesson 2 Transforming Trig Functions Essential Question: How can we use the amplitude, period, phase shift and vertical shift to transform the sine and cosine curves? Key Question: How do the values of A, B, H, and K impact the shape of the trigonometric functions?

Warm-Up/Activator Complete the Exploring Sine Graphs Activity and Report findings to the class.

Alternate Activator Graph each equation without a calculator Y = 2(x -3) 2 + 1y = - (x + 2) 2 - 3

Transformations: Vertical Shift: the vertical movement of the graph (“new” x-axis) Phase Shift: the horizontal movement of the graph (“new” y-axis) Period: the number of degrees or radians required to draw one complete cycle of the curve Amplitude: the distance the curve is from the “new” x-axis

Transformation Equation Amplitude and Inversion Period Combine to give Horizontal Movement Vertical Movement

Transformations Vertical shift– K Phase shift– the opp of H/B Period– sin and cos 360/B tan 180/B Amplitude-- |A| the sign indicates if it is inverted

Example 1 y = 2 cos (3x) amp = period = phase =vertical =

Example 2 y = cos (1/3x ) amp = period = phase =vertical =

Example 3 y = cos(4x) + 2 amp = period = phase =vertical =

Example 4 y = cos(x+ Π ) + 1 amp = period = phase =vertical =

Example 5 y = 3 sin(2x – Π) + 1 amp = period = phase =vertical =

Example 6 y = -sin(4x) – 2 amp = period = phase =vertical =

Example 7 y = ½ cos(2x) + 2 amp = period = phase =vertical =

Example 8 y =2 cos(1/2x+ Π ) – 1 amp = period = phase =vertical =

Chapter 4 - Lesson 3 Sinusoidal Regressions Essential Question: How can sinusoidal regressions be used to model periodic data? Key Question: How do you use the calculator to find sinusoidal regressions?

Your Turn