Trigonometry : Sin, Cos, Tan

Example Questions

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Example Question #1 : Sin, Cos, Tan

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

What is the cosine of ?

Explanation:

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

Therefore:

Example Question #2 : Sin, Cos, Tan

If  and , what is the value of ?

1

2

10

4

0.035

2

Explanation:

Example Question #1 : Trigonometric Operations

What is the value of ?

Explanation:

Solve each term separately.

Example Question #4 : Sin, Cos, Tan

Determine the value of .

Explanation:

Rewrite  in terms of sines and cosines.

Simplify the complex fraction.

Example Question #2 : Trigonometric Operations

Find the value of .

Explanation:

To find the value of , solve each term separately.

Sum the two terms.

Example Question #3 : Trigonometric Operations

Select the ratio that would give Tan B.

Explanation:

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

Example Question #3 : Trigonometric Operations

Calculate .

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 #7 : Sine, Cosine, Tangent

Calculate .

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 #1 : Sin, Cos, Tan

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

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 #5 : Trigonometric Operations

Round to the nearest hundredth.

None of the above