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Trigonometry : Trigonometric Operations

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Example Questions

Example Question #11 : Trigonometric Operations

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

Possible Answers:

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

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

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

$\small \sqrt{3}$

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

Correct answer:

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

Explanation:

Solution

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Example Question #12 : Trigonometric Operations

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

Possible Answers:

2.5

1.5

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 #2 : Trigonometry

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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Example Question #13 : Trigonometric Operations

Which of the following describes the ratio of sine?

Possible Answers:

$\frac{\text{opposite}}{\text{hypotenuse}}$

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

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

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

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

Correct answer:

$\frac{\text{opposite}}{\text{hypotenuse}}$

Explanation:

Sine is by definition of sides in a right triangle is opposite side over hypotenuse.

To remember this, use SOH CAH TOA.

SOH: Sine=Opposite/Hypotenuse

CAH: Cosine=Adjacent/Hypotenuse

TOA: Tangent=Opposite/Adjacent

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Example Question #1 : Secant, Cosecant, Cotangent

Find the value of the trigonometric function in fraction form for triangle ABC .

Triangle

What is the secant of $\angle A$ ?

Possible Answers:

7/25

$\frac{25}{24}$

25/7

24/25

24/7

Correct answer:

$\frac{25}{24}$

Explanation:

The value of the secant of an angle is the value of the hypotenuse over the adjacent.

Therefore:

$sec \angle A = \frac{hypotenuse}{adjacent} = \frac{25}{24}$

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Example Question #1 : Secant, Cosecant, Cotangent

Which of the following is the equivalent to $\frac{1}{\csc\theta}$ ?

Possible Answers:

$\sin\theta$

$\tan\theta\sin\theta$

$\cos\theta$

$\cot\theta$

$\sec\theta$

Correct answer:

$\sin\theta$

Explanation:

Since $\csc\theta=\frac{1}{\sin\theta}$ :

$\frac{1}{\csc\theta}=\frac{1}{\frac{1}{\sin\theta}}=1*\frac{\sin\theta}{1}=\sin\theta$

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Example Question #2 : Secant, Cosecant, Cotangent

Soh_cah_toa

For the above triangle, what is $\sec (\theta)$ if o = 8 , a = 15 and h = 17 ?

Possible Answers:

0.47

0.53

{}1.13

0.88

2.13

Correct answer:

{}1.13

Explanation:

Secant is the reciprocal of cosine.

$\sec \left ( \theta\right ) = \frac{1}{\cos \left ( \theta\right )}$

It's formula is:

$\sec(\theta) = \frac{\textup{hypotenuse}}{\textup{adjacent}}$

Substituting the values from the problem we get,

$\sec(\theta) = \frac{17}{15} = 1.13$

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Example Question #1 : Secant, Cosecant, Cotangent

Soh_cah_toa

For the above triangle, what is $\cot (\theta)$ if o = 18 , a = 24 and h = 30 ?

Possible Answers:

0.75

1.67

1.25

1.33

0.60

Correct answer:

1.33

Explanation:

Cotangent is the reciprocal of tangent.

$\cot \left ( \theta\right ) = \frac{1}{\tan \left ( \theta\right )}$

It's formula is:

$\cot(\theta) = \frac{\textup{adjacent}}{\textup{opposite}}$

Substituting the values from the problem we get,

$\cot(\theta) = \frac{24}{18} = 1.33$

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Example Question #5 : Secant, Cosecant, Cotangent

Determine the value of $cot(\frac{\pi}{4})$ .

Possible Answers:

$\infty$

$\frac{\sqrt2}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

Rewrite $cot(\frac{\pi}{4})$ in terms of sine and cosine.

$cot(\frac{\pi}{4})= \frac{cos(\frac{\pi}{4})}{sin(\frac{\pi}{4})}=\frac{\frac{\sqrt2}{2}}{\frac{\sqrt2}{2}}=1$

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Trigonometry : Trigonometric Operations

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #11 : Trigonometric Operations

Example Question #12 : Trigonometric Operations

Example Question #12 : Sin, Cos, Tan

Example Question #2 : Trigonometry

Example Question #13 : Trigonometric Operations

Example Question #1 : Secant, Cosecant, Cotangent

Example Question #1 : Secant, Cosecant, Cotangent

Example Question #2 : Secant, Cosecant, Cotangent

Example Question #1 : Secant, Cosecant, Cotangent

Example Question #5 : Secant, Cosecant, Cotangent

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