Q: Which of the following is NOT a valid trigonometric identity?

$$\tan \theta = \frac{1}{\csc \theta}$$

Q: Which of the following correctly expresses $$\tan \theta in $$terms of the sides of a right triangle?

$$\frac{\text{opposite}}{\text{adjacent}}$$

Q: Which of the following is the correct formula for converting degrees to radians?

$$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$

Q: Which of the following is the correct definition of $$\sec \theta in $$terms of a right triangle?

$$\frac{\text{hypotenuse}}{\text{adjacent}}$$

Question 1

Which of the following is NOT a valid trigonometric identity?

Accepted Answer

$$	an 	heta = \frac{1}{\csc 	heta}$$

Question 2

If a function $$f(x) is $$transformed to $$f(x) + c$$, what is the effect on its graph?

Accepted Answer

Vertical shift up by $$c$$ units

Question 3

Convert $$120^\circ to $$radians.

Accepted Answer

$$\frac{2\pi}{3}$$

Question 4

Given $$f(x) = 2\sin(3x - \frac{\pi}{4}) + 1$$, what is the amplitude of the function?

Accepted Answer

$$2$$

Question 5

Which transformation results in a reflection of the graph of $$f(x)$$ about the $$x-$$axis?

Accepted Answer

$$-f(x)$$

Question 6

What is the period of the function $$f(x) = \sin(5x)$$?

Accepted Answer

$$\frac{2\pi}{5}$$

Question 7

A Ferris wheel rotates such that a rider's height $$h (in $$meters) above the ground at time $$t (in $$minutes) is modeled by $$h(t) = 10\sin\left(\frac{\pi}{5}t\right) + 12. $$What is the maximum height reached by the rider?

Accepted Answer

$$22$$ meters

Question 8

Which of the following correctly expresses $$	an 	heta in $$terms of the sides of a right triangle?

Accepted Answer

$$\frac{	ext{opposite}}{	ext{adjacent}}$$

Question 9

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$f(x - \frac{\pi}{2})$$?

Accepted Answer

Shift right by $$\frac{\pi}{2}$$ units

Question 10

Which of the following is the correct formula for converting degrees to radians?

Accepted Answer

$$	ext{radians} = 	ext{degrees} 	imes \frac{\pi}{180}$$

Question 11

Given $$f(x) = \sin(x)$$, what is the effect of the transformation $$-f(x)$$?

Accepted Answer

Reflection about the $$x-$$axis

Question 12

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$f(-x)$$?

Accepted Answer

Reflection about the $$y-$$axis

Question 13

A sound wave is modeled by $$y = 3\sin(2x). $$What is the period of the wave?

Accepted Answer

$$\pi$$

Question 14

Which of the following is the correct definition of $$\sec 	heta in $$terms of a right triangle?

Accepted Answer

$$\frac{	ext{hypotenuse}}{	ext{adjacent}}$$

Question 15

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$f(x) - 2$$?

Accepted Answer

Vertical shift down by 2 units

Question 16

Which of the following is the correct formula for the vertical stretch of a function $$f(x) by a $$factor $$a$$?

Accepted Answer

$$a f(x)$$

Question 17

A temperature sensor records data modeled by $$T(t) = 5\cos(\pi t) + 20. $$What is the minimum temperature recorded?

Accepted Answer

$$15$$

Question 18

Which of the following is the correct formula for the period of $$f(x) = \sin(Bx)$$?

Accepted Answer

$$\frac{2\pi}{B}$$

Question 19

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$f(x + \pi)$$?

Accepted Answer

Shift left by $$\pi$$ units

Trigonometric Functions and Transformations: Precalculus Study Notes

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