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

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

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

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

Question 1

Which of the following is NOT a valid trigonometric identity?

Accepted Answer

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

Question 2

If $$f(x) = \sin(x)$$, what is the effect of the transformation $$f(x) + 3 on $$the graph?

Accepted Answer

Vertical shift up by 3 units

Question 3

Convert $$150^{\circ} to $$radians.

Accepted Answer

$$\frac{5\pi}{6}$$

Question 4

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

Accepted Answer

$$-f(x)$$

Question 5

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

Accepted Answer

$$2$$

Question 6

What is the period of the function $$f(x) = \sin(4x)$$?

Accepted Answer

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

Question 7

Which of the following describes a horizontal shift to the left by $$c$$ units for $$f(x)$$?

Accepted Answer

$$f(x + c)$$

Question 8

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

Accepted Answer

Reflection about the $$y-$$axis

Question 9

A Ferris wheel rotates such that the height $$h (in $$meters) of a seat above the ground at time $$t (in $$seconds) is modeled by $$h(t) = 10\sin\left(\frac{\pi}{15}t\right) + 12. $$What is the maximum height reached by the seat?

Accepted Answer

$$22$$ meters

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

Vertical stretch by a factor of 2

Question 12

Which transformation compresses the graph of $$f(x)$$ horizontally by a factor of 3?

Accepted Answer

$$f(3x)$$

Question 13

Convert $$\frac{\pi}{3}$$ radians to degrees.

Accepted Answer

$$60^{\circ}$$

Question 14

Given $$f(x) = \sin(x)$$, which transformation results in a vertical shift down by 4 units?

Accepted Answer

$$f(x) - 4$$

Question 15

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

Accepted Answer

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

Question 16

A sound wave can be modeled by $$y(t) = 0.5\sin(440\pi t). $$What is the amplitude of this wave?

Accepted Answer

$$0.5$$

Question 17

Which transformation results in a shift of the graph of $$f(x) to $$the right by $$c$$ units?

Accepted Answer

$$f(x - c)$$

Question 18

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

Accepted Answer

Vertical shift down by 2 units

Question 19

Which of the following is the correct definition of $$\csc 	heta$$?

Accepted Answer

$$\frac{1}{\sin 	heta}$$

Precalculus Study Notes: Trigonometric Functions, Identities, and Transformations

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