Int. Trig. Name: _____________________________ Weekend Practice ‐ Analyzing Trig Functions Amplitude Trig Function Omega, ω Y= (Distance from Midline) sin or cos ω=
2
Pd
Date: ____________________ Pd: ______ X or ϴ C Vertical Shift (VARIABLE) C= ‐(PS)(ω) (MIDLINE) Write the equation of the trigonometric function with the given characteristics. 1. Sine Function; Amplitude=5; Vertical Reflection; Period=π; Phase Shift is LEFT 3 units; Midline at y=0 y = ‐5sin(2x+6) 2. Cosine Function; Amplitude=3; Period=4π; Phase Shift is RIGHT π units; Midline at y=4 y = 3 cos( x
)+4 3. Cosine Function; Minimum value = ‐3; Maximum value = 3; Period=3π; Vertical Shift down 5; No Phase Shift y = 3 cos ( x) 4. Sine Function; Minimum value = ‐5; Maximum value = 1; Period=π; Phase Shift is LEFT 4π y = 3 sin (2x+8 ) ‐ 2 5. Secant Function; Amplitude is 0.5; Period=
2
2
; Vertical Shift Up 2 units; Phase Shift Right 3
3
6. Cosecant Function; Local Minimum is 7; Local Maximum 3; Period is π; No Phase Shift 7. Tangent Function; Amplitude is 5; Period=  ; Vertical Shift Up 9 units; No Phase Shift. 8. Cotangent Function; Phase shift left y = cot ( x
) ‐ 3 
4
; Peroid = 2 ; vertical shift down 3 Analyze Real‐World Sinusoidal Functions. Read the given statements and answer the questions that follow.  
m   10 6 
1. The amount of daylight (hrs) in Quito, Ecuador can be represented by the equation d  2 cos 
(where m=1 represents January 1st, m=2 represents February 1st, etc.) a. What is the maximum amount of daylight in Quito?
Max = 12 hrs Min = 8 hrs b. What is the minimum amount of daylight in Quito? c. When does the maximum amount of daylight occur? (Find Month) SEE Graph (x = 0 and x = 12) d. When does the minimum daylight occur? (Find Month) SEE Graph (x=6) e. Graph what is going on here. 12 10 8
3 9 12 6 2. A ferris wheel with center 50 feet above the ground has a maximum height of 90 feet. It takes 5 minutes for the ferris wheel to make a full rotation a. Draw a picture of what is happening. 90 ft 50 ft 10 ft 1.25 3.75
5 2.5 10 ft b. How far off the ground must the riders be to get on the ride (Min)? 2 min 30 sec c. How long does it take for the riders to reach the maximum? Y = ‐40 cos Write an equation for the situation. 50 ft d. What is the height of a rider after 3 min 45 sec? 1 min 15 sec e. How long does it take a rider to reach a height of 50 feet?