3) 0.96) –0.99) –3/412) –0.6 15) 2 cycles; a = 2; Period = π 18) y = 4 sin (½x) 21) y = 1.5 sin (120x) 24) 27) 30) Period = π; y = 2.5 sin(2x) 33) Period = 4; y = 3 sin(90x)

The Cosine Function

 Traces x – coordinate values of the unit circle  Period of 360° or 2π  Amplitude of 1  Begins at its maximum max, zero, min, zero, max 1 360° 2 π

The Sine CurveThe Cosine Curve List the similarities and differences between these two curves.

 Amplitude = |a|  Period = or 360° b 2πb2πb

Sketch a cosine curve that has the following: 1) Amplitude of 2 2) Period of 720° Assume a > °

Writing  With given information we can write equations to model a situation  The amplitude is half of a given wave height  The b value can be found by solving P = for the given period Writing the Waves Write a cosine function to model 10 in. waves that occur every 4 seconds. 1) a = 10/2 = 5 2) P = 2π/b 4 = 2π/b b = 2π/4 b = π/2 So, y = 5 cos ((π/2)θ) 2πb2πb

We can use the intersect feature of the calculator to find certain values Solve 3 = 5 cos ((π/2)x) for 0 ≤ x ≤ 2π 1) Graph y 1 = 3 2) Graph y 2 = 5 cos ((π/2)x) 3) Set window [0, 2π] by [-4, 4] 4) Use, to find the intersections x ≈ 0.59 x ≈ 3.41 x ≈ 4.59

 For tomorrow, complete exercises 1 – 21 odd, starting on page 732