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Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Trigonometric Functions And Graphs

What is the period of

$\tan \left ( \frac{x}{\pi } \right )$ ?

Possible Answers:

$\frac{1}{\pi }$

$\pi$

$\pi^{2}$

$2\pi$

Correct answer:

$\pi^{2}$

Explanation:

The period for $\tan(x)$ is $\pi$ . However, if a number is multiplied by , you divide the period $\pi$ by what is being multiplied by . Here, $(1/\pi )$ is being multiplied by . $\pi/(1/\pi )$ equals $\pi^{2}$ .

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Example Question #1 : Trigonometric Functions And Graphs

Which of the following is not in the range of the function $y = \sin{x}$ ?

Possible Answers:

$\frac{3}{4}$

$\frac{3}{2}$

$\frac{2}{3}$

$-\frac{1}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

The range of the function $y= \sin x$ is all numbers between and (the sine wave never goes above or below this).

Of the choices given, $\frac{3}{2}$ is greater than and thus not in this range.

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Example Question #2 : Trigonometric Identities

Trig_id

What is the $\sin$ of $\theta$ ?

Possible Answers:

$\frac{o}{a}$

$\frac{h}{a}$

$\frac{h}{o}$

$\frac{a}{h}$

$\frac{o}{h}$

Correct answer:

$\frac{o}{h}$

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: SOHCAHTOA .

$\sin=\frac{opposite}{hypotenuse}$

$\cos=\frac{adjacent}{hypotenuse}$ ,

$\tan=\frac{opposite}{adjacent}$

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

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Example Question #1 : Trigonometric Identities

Trig_id

What is the $\cos$ of $\theta$ ?

Possible Answers:

$\frac{h}{a}$

$\frac{o}{h}$

$\frac{h}{o}$

$\frac{a}{h}$

$\frac{o}{a}$

Correct answer:

$\frac{a}{h}$

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: SOHCAHTOA .

$\sin=\frac{opposite}{hypotenuse}$

$\cos=\frac{adjacent}{hypotenuse}$ ,

$\tan=\frac{opposite}{adjacent}$

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

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Example Question #1 : Solving Trigonometric Equations

In a right triangle, if

$cos(x)=\frac{3}{5}$

and

$cos(y)=\frac{4}{5}$

then what does $\tan(x)$ equal?

Possible Answers:

$\frac{4}{3}$

$\frac{5}{4}$

$\frac{3}{5}$

$\frac{3}{4}$

Correct answer:

$\frac{4}{3}$

Explanation:

One can draw a right triangle with acute angles $\angle x$ and $\angle y$ . The side adjacent to $\angle y$ is 4, and the side adjacent to $\angle x$ is 3.

$tan(x)=\frac{opposite}{adjacent}$

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Example Question #71 : Pre Calculus

Bob manages a pizza store. He bought a new machine that tracks how big his employees are cutting the pizza slices. The machine measures the average angle size of each slice of each pizza. Unfortunately, the angle is given as 0.7854 radians which Bob does not understand. Help Bob by converting the radian angle into degrees. In degrees, what is the size of the angle for an average pizza slice.

Possible Answers:

$25^{\circ}$

$60^{\circ}$

$30^{\circ}$

$45^{\circ}$

$75^{\circ}$

Correct answer:

$45^{\circ}$

Explanation:

To convert we use a common conversion amount. It may be easiest to remember the full circle example. In degrees, a full circle is $360^{\circ}$ around. In terms of radians, a full circle is $2\pi$ . So to get our answer

$0.7854\ \text{Radians} *\frac{360^{\circ}}{2\pi\ \text{Radians}}= 45^{\circ}$

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Example Question #72 : Pre Calculus

Convert $120^{\circ}$ into radians.

Possible Answers:

$\frac{4\pi }{3}$

$\pi$

$2\pi$

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

$\frac{3\pi }{4}$

Correct answer:

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

Explanation:

To convert from degrees to radians, one multiplies by $\frac{\pi }{180}$ .

$120\cdot \frac{\pi }{180}=\frac{2\pi}{3}$

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Example Question #73 : Pre Calculus

In the unit circle, what is the angle in radians that corresponds to the point (0, -1)?

Possible Answers:

$\frac{\pi }{2}$

$\pi$

$2\pi$

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

Correct answer:

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

Explanation:

On the unit circle, (0,-1) is the point that falls between the third and fourth quadrant. This corresponds to $\frac{3\pi }{2}$ .

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Example Question #74 : Pre Calculus

What is the reference angle for $\frac{16\pi}{3}$ ?

Possible Answers:

$\frac{3\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{6}$

$\frac{4\pi}{3}$

Correct answer:

$\frac{4\pi}{3}$

Explanation:

To find the reference angle, subtract $2\pi$ (1 trip around the unit circle) from the given angle until you reach an angle which is less than $2\pi$ .

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Example Question #5 : Using The Unit Circle

What is $\sin(\pi)$ ?

Possible Answers:

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{\sqrt{2}}{2}$

Correct answer:

Explanation:

If you examine the unit circle, you'll see that that $\sin(\pi)=0$ .

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Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Trigonometric Functions And Graphs

Example Question #1 : Trigonometric Functions And Graphs

Example Question #2 : Trigonometric Identities

Example Question #1 : Trigonometric Identities

Example Question #1 : Solving Trigonometric Equations

Example Question #71 : Pre Calculus

Example Question #72 : Pre Calculus

Example Question #73 : Pre Calculus

Example Question #74 : Pre Calculus

Example Question #5 : Using The Unit Circle

All Precalculus Resources

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