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  2. AP Pre Calculus
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Trigonometric and Polar Functions

Question 1
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 2
college-boardPre-CalculusAPExam Style
1 mark

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

Question 3
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 4
college-boardPre-CalculusAPExam Style
1 mark

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

Question 5
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 6
college-boardPre-CalculusAPExam Style
1 mark

What is the maximum value of the sine function?

Question 7
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?

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Question 8
college-boardPre-CalculusAPExam Style
1 mark

If the function f(t)=A⋅cos⁡(Bt−C)+Df(t) = A \cdot \cos(Bt - C) + Df(t)=A⋅cos(Bt−C)+D models the height of a tide over time, what does the variable 'A' represent?

Question 9
college-boardPre-CalculusAPExam Style
1 mark

When modeling daily temperatures using a sinusoidal function, what does the horizontal shift CB\frac{C}{B}BC​ represent?

Question 10
college-boardPre-CalculusAPExam Style
1 mark

What does 'B' represent in a sinusoidal function formula like f(x)=Asin⁡(Bx)f(x) = A \sin(Bx)f(x)=Asin(Bx)?