Trigonometry : Sin, Cos, Tan

Study concepts, example questions & explanations for Trigonometry

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Example Questions

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Example Question #1 : Trigonometric Operations

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

Triangle

What is the cosine of ?

Possible Answers:

Correct answer:

Explanation:

The cosine of an angle is the value of the adjacent side over the hypotenuse.

Therefore:

Example Question #2 : Trigonometric Operations

If  and , what is the value of ?

Possible Answers:

1

2

0.035

4

10

Correct answer:

2

Explanation:

Example Question #3 : Trigonometric Operations

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Solve each term separately.

Add both terms.

Example Question #4 : Trigonometric Operations

Determine the value of .

Possible Answers:

Correct answer:

Explanation:

Rewrite  in terms of sines and cosines.

Simplify the complex fraction.

Example Question #5 : Trigonometric Operations

Find the value of .

Possible Answers:

Correct answer:

Explanation:

To find the value of , solve each term separately.

Sum the two terms.

Example Question #6 : Trigonometric Operations

Select the ratio that would give Tan B. 10

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

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

  

Example Question #1 : Sin, Cos, Tan

Calculate .

Possible Answers:

Correct answer:

Explanation:

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

for all .

Since , we can rewrite the original expression  as follows:

                 

                 

                 

                 

Hence, 

Example Question #8 : Trigonometric Operations

Calculate .

Possible Answers:

Correct answer:

Explanation:

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

Next, recall that  lies in the fourth quadrant of the unit circle, wherein the cosine is positive. Furthermore, the reference angle of  is 

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

,

which is .

Therefore,

Example Question #2 : Sin, Cos, Tan

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

Possible Answers:

Correct answer:

Explanation:

Because  is an odd function, we can rewrite the second term in the expression.

.

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

.

Because they are reciprocals, .

Example Question #10 : Trigonometric Operations

Round to the nearest hundredth. 

Use your calculator to find:

 

Possible Answers:

None of the above

Correct answer:

Explanation:

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

Plug in  which equals to .

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