Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Trigonometry

Trig_id

What is  if  and ?

Possible Answers:

Correct answer:

Explanation:

In order to find  we need to utilize the given information in the problem.  We are given the opposite and adjacent sides.  We can then, by definition, find the  of  and its measure in degrees by utilizing the  function.

Now to find the measure of the angle using the  function.

If you calculated the angle's measure to be  then your calculator was set to radians and needs to be set on degrees.

Example Question #3 : Graphs And Inverses Of Trigonometric Functions

Trig_id

If  equals  and  is , how long is 

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

This problem can be easily solved using trig identities.  We are given the hypotenuse  and .  We can then calculate side  using the .

Rearrange to solve for .

If you calculated the side to equal  then you utilized the  function rather than the .

Example Question #4 : Graphs And Inverses Of Trigonometric Functions

Triangle

What is the length of CB?

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : Graphs And Inverses Of Trigonometric Functions

Rt_triangle_letters

In this figure, angle . If side  and , what is the value of angle ?

Possible Answers:

Undefined

Correct answer:

Explanation:

For this problem, use the law of sines:

.

In this case, we have values that we can plug in:

Example Question #1 : Applying The Law Of Sines

Rt_triangle_lettersIn this figure, if angle , side , and side , what is the value of angle ?

(NOTE: Figure not necessarily drawn to scale.)

Possible Answers:

Undefined

Correct answer:

Explanation:

First, observe that this figure is clearly not drawn to scale. Now, we can solve using the law of sines:

.

In this case, we have values that we can plug in:

Example Question #1 : Triangles

Rt_triangle_letters

In this figure, if angle , side , and side , what is the measure of angle ?

Possible Answers:

Undefined

Correct answer:

Explanation:

Since , we know we are working with a right triangle.

That means that .

In this problem, that would be:

Plug in our given values:

Example Question #7 : Graphs And Inverses Of Trigonometric Functions

Rt_triangle_letters

In this figure, , and . What is the value of angle ?

Possible Answers:

Undefined

Correct answer:

Explanation:

Notice that these sides fit the pattern of a 30:60:90 right triangle: .

In this case, .

Since angle  is opposite , it must be .

Example Question #8 : Graphs And Inverses Of Trigonometric Functions

A triangle has angles of . If the side opposite the angle is , what is the length of the side opposite ?

Possible Answers:

Correct answer:

Explanation:

The pattern for is that the sides will be .

If the side opposite is , then the side opposite will be .

Example Question #11 : Graphs And Inverses Of Trigonometric Functions

A triangle has sides of length 12, 17, and 22. Of the measures of the three interior angles, which is the greatest of the three?

Possible Answers:

Correct answer:

Explanation:

We can apply the Law of Cosines to find the measure of this angle, which we will call :

 

The widest angle will be opposite the side of length 22, so we will set:

 

 

Example Question #12 : Graphs And Inverses Of Trigonometric Functions

In  , , and . To the nearest tenth, what is ?

Possible Answers:

A triangle with these characteristics cannot exist.

Correct answer:

Explanation:

By the Law of Cosines:

or, equivalently,

Substitute:

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