Precalculus : Find the value of any of the six trigonometric functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Find The Value Of Any Of The Six Trigonometric Functions

Solve the following:  

Possible Answers:

Correct answer:

Explanation:

Rewrite  in terms of sine and cosine functions.

Since these angles are special angles from the unit circle, the values of each term can be determined from the x and y coordinate points at the specified angle.  

Solve each term and simplify the expression.

Example Question #2 : Find The Value Of Any Of The Six Trigonometric Functions

Q1 new

Find the value of .

Possible Answers:

Correct answer:

Explanation:

Using trigonometric relationships, one can set up the equation

.

Solving for ,

Thus, the answer is found to be 29.

Example Question #1 : Find The Value Of Any Of The Six Trigonometric Functions

Q2 new

Find the value of .

Possible Answers:

Correct answer:

Explanation:

Using trigonometric relationships, one can set up the equation

.

Plugging in the values given in the picture we get the equation,

.

Solving for ,

.

Thus, the answer is found to be 106.

Example Question #4 : Find The Value Of Any Of The Six Trigonometric Functions

Find all of the angles that satistfy the following equation:

Possible Answers:

OR 

 

Correct answer:

OR 

Explanation:

The values of  that fit this equation would be:

 and  

because these angles are in QI and QII where sin is positive and where

.

This is why the answer 

is incorrect, because it includes inputs that provide negative values such as:

Thus the answer would be each  multiple of  and  , which would provide the following equations:

  OR    

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