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  2. AP Pre Calculus
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Trigonometric and Polar Functions

Question 1
college-boardPre-CalculusAPExam Style
1 mark

Which transformation does not correspond to the change from f(x)=cos(x)f(x) = \\cos(x)f(x)=cos(x) to g(x)=cos(x+pi)g(x) = \\cos(x + \\pi)g(x)=cos(x+pi)?

Question 2
college-boardPre-CalculusAPExam Style
1 mark

What transformation occurs when you replace 'sin' with '-sin' in the sine function f(x)=sin(kx)f(x) = \\sin(kx)f(x)=sin(kx)?

Question 3
college-boardPre-CalculusAPExam Style
1 mark

What is the period of the inverse function for y = cos(2x)?

Question 4
college-boardPre-CalculusAPExam Style
1 mark

What is the amplitude of the sinusoidal function f(x)=−3sin⁡(4x+π6)f(x) = -3\sin(4x + \frac{\pi}{6})f(x)=−3sin(4x+6π​) when compared to its parent function y=sin⁡(x)y=\sin(x)y=sin(x)?

Question 5
college-boardPre-CalculusAPExam Style
1 mark

Which function has a vertical shift downward compared to y = sin(x)?

Question 6
college-boardPre-CalculusAPExam Style
1 mark

What is the maximum value of the sine function?

Question 7
college-boardPre-CalculusAPExam Style
1 mark

For g(t)=−2cos⁡(t4−π)g(t) = -2\cos\left(\frac{t}{4} - \pi\right)g(t)=−2cos(4t​−π), which transformation applied to its parent function would produce an inverse with equal amplitude?

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Question 8
college-boardPre-CalculusAPExam Style
1 mark

If the amplitude of a sinusoidal function is tripled and the period is halved, how does this affect the graph of the original function?

Question 9
college-boardPre-CalculusAPExam Style
1 mark

The population of a seasonal species in a certain habitat oscillates following a sinusoidal model P(t)=Acos(B(t−C))+DP(t) = A \\cos(B(t - C)) + DP(t)=Acos(B(t−C))+D; if scientists determine that A=500A=500A=500, B=pi/6B=\\pi/6B=pi/6, and D=1500D=1500D=1500 describe one characteristic of this population throughout its cycle?

Question 10
college-boardPre-CalculusAPExam Style
1 mark

If the period of a sinusoidal function f(x) = A sin(Bx + C) + D is increased by a factor of 3, what transformation would have been applied to the original value of B?