Precalculus : Fundamental Trigonometric Identities

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #31 : Fundamental Trigonometric Identities

Let , , and  be real numbers. Given that:

What is the value of  in function of ?

Possible Answers:

Correct answer:

Explanation:

We note first, using trigonometric identities that: 

This gives:

Since, 

We have :

Example Question #31 : Fundamental Trigonometric Identities

Using the fact that,

 .

What is the result of the following sum:

Possible Answers:

Correct answer:

Explanation:

We can write the above sum as :

 

From the given fact, we have :

and we have : .

 

 

This gives :

 

 

Example Question #33 : Fundamental Trigonometric Identities

Compute  in function of .

Possible Answers:

Correct answer:

Explanation:

Using trigonometric identities we have :

 and we know that:

This gives us :

Hence:

Example Question #34 : Fundamental Trigonometric Identities

Given that :

Let,

What is  in function of ?

Possible Answers:

Correct answer:

Explanation:

We will use the given formula :

We have in this case:

 

Since we know that :

 

This gives :

Example Question #35 : Fundamental Trigonometric Identities

Using the fact that  , what is the result of the following sum:

 
Possible Answers:

Correct answer:

Explanation:

We can write the above sum as :

From the given fact, we have :

This gives us :

 

Therefore we have:

 

Example Question #36 : Fundamental Trigonometric Identities

Let be real numbers. If  and

What is the value of in function of   ?

Possible Answers:

Correct answer:

Explanation:

Using trigonometric identities we know that :

This gives :

We also know that 

This gives :

 

Example Question #37 : Fundamental Trigonometric Identities

Given that :

 and,

Compute :

 in function of .

Possible Answers:

Correct answer:

Explanation:

We have using the given result:

This gives us:

Hence :

Example Question #38 : Fundamental Trigonometric Identities

Let  be an integer and  a real number. Compute  as a function of .

Possible Answers:

Correct answer:

Explanation:

Using trigonometric identities we have :

We know that :

 and 

This gives :

Example Question #39 : Fundamental Trigonometric Identities

Compute .

Possible Answers:

Correct answer:

Explanation:

Using trigonometric identities we know that:

Letting  and  in the above expression we have:

We also know that:

 and .

This gives:

Example Question #40 : Fundamental Trigonometric Identities

Given that:

, what is the value of  in function of ?

Possible Answers:

Correct answer:

Explanation:

We know by definition that:

We also have by trigonometric identities:

 

Thus :

Now we have:

This gives us:

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