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Trigonometry : Trigonometry

Study concepts, example questions & explanations for Trigonometry

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6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Sin, Cos, Tan

Select the ratio that would give Tan B.

Possible Answers:

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

$\tan B=\frac{AC}{AB}$

None of the other answers.

$\tan B=\frac{AB}{AC}$

$\tan B=\frac{CB}{AC}$

Correct answer:

$\tan B=\frac{AC}{AB}$

Explanation:

We need the Tan B. Which side lengths correspond to this ratio?

$\tan=\frac{opp}{adj}$

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Example Question #11 : Trigonometry

Calculate $tan(\frac{4\pi}{3})$ .

Possible Answers:

$\sqrt{3}$

$-\sqrt{3}$

Correct answer:

$\sqrt{3}$

Explanation:

The tangent function has a period of $\pi$ units. That is,

$tan(x+n\pi)=tanx$

for all $n\in\mathbb{Z}$ .

Since $\frac{4\pi}{3}=\frac{\pi}{3}+\pi$ , we can rewrite the original expression $tan(\frac{4\pi}{3})$ as follows:

$tan(\frac{4\pi}{3})=tan(\frac{\pi}{3}+\pi)$

$=tan(\frac{\pi}{3})$

$=\frac{sin(\frac{\pi}{3})}{cos(\frac{\pi}{3})}$

$=\frac{(\frac{\sqrt{3}}{2})}{(\frac{1}{2})}$

$=\sqrt{3}$

Hence,

$tan(\frac{4\pi}{3})=\sqrt{3}$

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Example Question #2 : Sin, Cos, Tan

Calculate $cos(\frac{5\pi}{3})$ .

Possible Answers:

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

$-\frac{1}{2}$

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

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

First, convert the given angle measure from radians to degrees:

$cos(\frac{5\pi}{3})=cos(300^{\circ})$

Next, recall that $300^{\circ}$ lies in the fourth quadrant of the unit circle, wherein the cosine is positive. Furthermore, the reference angle of $300^{\circ}$ is

$360^{\circ}-300^{\circ}=60^{\circ}$

Hence, all that is required is to recognize from these observations that

$cos(\frac{5\pi}{3})=cos(300^{\circ}) =cos(60^{\circ})$ ,

which is $\frac{1}{2}$ .

Therefore,

$cos(\frac{5\pi}{3})=\frac{1}{2}$

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Example Question #2 : Sin, Cos, Tan

What is the result when the following expression is simplified as much as possible?

$\sin(2h)\sec(h)+2\sin(-h)$

Possible Answers:

$2\sin h$

$\sec h$

Correct answer:

Explanation:

Because $\sin x$ is an odd function, we can rewrite the second term in the expression.

$2\sin(-h)=-2\sin h$ .

We now use a double-angle formula to expand the first term.

$\sin(2h)\sec h=2\sin h\cos h\sec h$ .

Because they are reciprocals, $\cos h\sec h=1$ .

$2\sin h\cos h\sec h-2\sin h=2\sin h-2\sin h=0.$

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Example Question #1 : Sine, Cosine, & Tangent

Round to the nearest hundredth.

Use your calculator to find:

$\sin72^{\circ}$

Possible Answers:

None of the above

0.95

0.72

0.25

Correct answer:

0.95

Explanation:

Before plugging the function into the calculator make sure the mode of the calculator is set to degrees,

Plug in $\sin72^{\circ}$ which equals to 0.95 .

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Example Question #1 : Sin, Cos, Tan

Round to the nearest hundredth.

Use your calculator to find:

$\cos \frac{3\pi}{8}$

Possible Answers:

0.38

None of the above

0.95

Correct answer:

0.38

Explanation:

Before plugging the function into the calculator make sure the mode of the calculator is set to radians,

plug in

$\cos \frac{3\pi}{8}$

which is equal to 0.38 .

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Example Question #11 : Sin, Cos, Tan

What is the value of cos30^o . sin30^o . tan60^o

Possible Answers:

$\small \frac{\sqrt{3}}{4}$

$\small \frac{3}{4}$

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

$\small \frac{1}{2}$

$\small \sqrt{3}$

Correct answer:

$\small \frac{3}{4}$

Explanation:

Solution

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Example Question #11 : Sine, Cosine, & Tangent

$\left ( \sin15 + \cos\15 \right )^{2}$ What is the closest value to this expression?

Possible Answers:

1.5

2.5

Correct answer:

1.5

Explanation:

First you have to know the equation for $\left ( a+b\right )^{2} = a^{2}+2ab+b^{2}$ and apply it to our equation. Second the formula of $\sin^{2}+\cos^{2}=1$ will allow you to get rid of the square sin and cos. Third the equation $\sin2x = 2\sin \cos$ will allow you to get rid of the 2ab . Therefore, we will have a $\sin(30)$ , and that will be equal to 0.5 . Sum and 0.5 and you will get 1.5

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Example Question #12 : Sin, Cos, Tan

if $\cos x = \frac{4}{5}$ What is $\sin2x$ ?

Possible Answers:

$\frac{3}{5}$

$\frac{5}{13}$

$\frac{7}{25}$

$\frac{12}{13}$

$\frac{24}{25}$

Correct answer:

$\frac{7}{25}$

Explanation:

Remember two things. First if $\cos x=\frac{4}{5}$ , find the $\sin(x)$ by using the Pythagoras Theorem. If one side is and the hypotenuse is , then the other side is . $\sin x$ will be $\frac{3}{5}$ . Finally remember the formula for $\sin2x = 2\sin x *\cos x$ . And just place the things we found to the equation.

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Example Question #614 : New Sat

If cos x = 0.2 $\small \cosx$ and sin x = 0.4, what is the value of tan x?

Possible Answers:

0.035

Correct answer:

Explanation:

$\small \tan{x}=\frac{\sin{x}}{\cos{x}}$

$\small \small \tan{x}=\frac{0.4}{0.2}$

$\small \tan{x}=0.035$

$\small x=\tan^{-1}0.035$

$\small x=2$

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Trigonometry : Trigonometry

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Sin, Cos, Tan

Example Question #11 : Trigonometry

Example Question #2 : Sin, Cos, Tan

Example Question #2 : Sin, Cos, Tan

Example Question #1 : Sine, Cosine, & Tangent

Example Question #1 : Sin, Cos, Tan

Example Question #11 : Sin, Cos, Tan

Example Question #11 : Sine, Cosine, & Tangent

Example Question #12 : Sin, Cos, Tan

Example Question #614 : New Sat

All Trigonometry Resources

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