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High School Math : Trigonometry

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Example Questions

Example Question #1 : Graphing The Sine And Cosine Functions

Trig_id

If $\theta$ equals $55^{\circ}$ and is 15ft , how long is ?

Possible Answers:

8.6ft

13.2ft

Not enough information to solve

12.3ft

11.3ft

Correct answer:

12.3ft

Explanation:

This problem can be easily solved using trig identities. We are given the hypotenuse (15ft) and $\theta (55^{\circ})$ . We can then calculate side using the $\sin$ .

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

$\sin55^{\circ}=\frac{o}{15ft}$

Rearrange to solve for .

$o=\sin55^{\circ}*15ft$

$\dpi{100} \rightarrow 12.3ft$

If you calculated the side to equal 8.6ft then you utilized the $\cos$ function rather than the $\sin$ .

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Example Question #4 : Finding Sides

Triangle

What is the length of CB?

Possible Answers:

$\frac{AB}{\sin A}$

$\frac{\tan C}{AB}$

$\frac{\sin B}{AC}$

$\frac{AB}{\tan C}$

$\frac{AC}{\sin A}$

Correct answer:

$\frac{AB}{\tan C}$

Explanation:

$\tan X= \frac{OPPOSITE}{ADJACENT}$

$\tan C=\frac{AB}{CB}$

$CB= \frac{AB}{\tan C}$

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Example Question #1 : Trigonometric Equations

If $tanx=\frac{1}{3}$ , find $f(x)=\frac{sin(3\pi +x)+sin(x-\frac{\pi }{2})}{cos(x-\pi )+cos(\frac{3\pi }{2}+x)}$ .

Possible Answers:

-2

-1

Correct answer:

Explanation:

First we need to simplify each term:

$sin(3\pi +x)= -sinx$

$sin(x-\frac{\pi }{2})=cosx$

$cos(x-\pi )=- cosx$

$cos(\frac{3\pi }{2}+x)=sinx$

So we will have:

$f(x)=\frac{-sinx-cosx}{-cosx+sinx}$

Since we have the value of tanx , we can divide the numerator and denominator by cosx .

$f(x)=\frac{-\frac{sinx}{cosx}-\frac{cosx}{cosx}}{\frac{-cosx}{cosx}+\frac{sinx}{cosx}}=\frac{-tanx-1}{-1+tanx} = \frac{1+tanx}{1-tanx}$

We can then substitute the value of tanx in the obtained function.

$f(x)=\frac{1+\frac{1}{3}}{1-\frac{1}{3}}=\frac{\frac{4}{3}}{\frac{2}{3}}=2$

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Example Question #2 : Solving Trigonometric Equations

A right triangle has an angle of $41^\circ$ . If the side opposite it has a length of , what is the hypotenuse?

Possible Answers:

6.04

9.2

5.25

10.6

12.19

Correct answer:

12.19

Explanation:

For this problem we will use the sine function as $\sin=\frac{O}{H}$ .

Plug in our given information:

$\sin(41^\circ)=\frac{8}{H}$

$H=\frac{8}{\sin(41^\circ)}$

H=12.19

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Example Question #3 : Solving Trigonometric Equations

A right triangle has an angle of $72^\circ$ . If the side adjacent to it has a length of , what is the hypotenuse?

Possible Answers:

3.4

35.6

10.46

11.56

3.57

Correct answer:

35.6

Explanation:

For this problem we will use the cosine function as $\cos=\frac{A}{H}$ .

Plug in our given information:

$\cos(72^\circ)=\frac{11}{H}$

$H=\frac{11}{\cos(72^\circ)}$

H=35.6

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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:

$\frac{3}{5}$

$\frac{3}{4}$

$\frac{5}{4}$

$\frac{4}{3}$

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 #1 : Trigonometric Equations

If $sinx-cosx=\frac{1}{3}$ , find the value of the function $f(x)=sin^{3}x+cos^{3}x$ .

Possible Answers:

$\frac{13}{27}$

$-\frac{13}{27}$

$\frac{11}{27}$

$-\frac{11}{27}$

Correct answer:

$\frac{13}{27}$

Explanation:

We can write:

$sinx-cosx=\frac{1}{3}$

$\Rightarrow (sinx-cosx)^{2}=\frac{1}{9}$

$\Rightarrow sin^2x+cos^2x-2sinxcosx=\frac{1}{9}$

$\Rightarrow 2sinxcosx=1-\frac{1}{9}$

$\Rightarrow sinxcosx=\frac{4}{9}$

We can also write:

(sinx-cosx)^3=sin^3x+cos^3x+3sinxcos^2x-3cosxsin^2x

$\Rightarrow sin^3x+cos^3x=(sinx-cosx)^3+3sinxcosx(sinx-cosx)$

Now we can substitute the values of (sinx - cosx) and (sinx * cosx) in the obtained function:

$\Rightarrow sin^3x+cos^3x=(\frac{1}{3})^3+3*\frac{4}{9}*\frac{1}{3}=\frac{1}{27}+\frac{4}{9}=\frac{13}{27}$

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Example Question #72 : Pre Calculus

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

Possible Answers:

$\frac{3}{4}$

$\frac{2}{3}$

$-\frac{1}{2}$

$\frac{3}{2}$

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 #1 : Trigonometric Functions And Graphs

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$

Possible Answers:

cosx

$\frac{1-x}{2}$

$\frac{1+x}{2}$

$\frac{x}{2}$

Correct answer:

$\frac{1+x}{2}$

Explanation:

We need to use the following formulas:

a) $cos^2x=\frac{1+cos2x}{2}$

and

b) $cos(cos^{-1}x)=x$

We can simplify f(x) as follows:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)=\frac{1+cos(cos^{-1}x)}{2}=\frac{1+x}{2}$

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Example Question #1 : Understanding Period And Amplitude

What is the period of

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

Possible Answers:

$\pi^{2}$

$\frac{1}{\pi }$

$\pi$

$2\pi$

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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High School Math : Trigonometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Graphing The Sine And Cosine Functions

Example Question #4 : Finding Sides

Example Question #1 : Trigonometric Equations

Example Question #2 : Solving Trigonometric Equations

Example Question #3 : Solving Trigonometric Equations

Example Question #1 : Solving Trigonometric Equations

Example Question #1 : Trigonometric Equations

Example Question #72 : Pre Calculus

Example Question #1 : Trigonometric Functions And Graphs

Example Question #1 : Understanding Period And Amplitude

All High School Math Resources

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