Precalculus : Solve Trigonometric Equations and Inequalities

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Solving Trigonometric Equations And Inequalities

Use trigonometric identities to solve the following equation for :

Possible Answers:

Correct answer:

Explanation:

Use the trigonometric identities to switch sec into terms of tan:

hence,

 

So we have , making 

Therefore the solution is  for n being any integer.

Example Question #2 : Solving Trigonometric Equations And Inequalities

Which of the following is not a solution to   for 

Possible Answers:

Correct answer:

Explanation:

We begin by setting the right side of the equation equal to 0.

The equation might be easier to factor using the following substitution.

This gives the following

This can be factored as follows

Therefore

Replacing our substitution therefore gives

Within our designated domain, we get three answers between our two equations.

       when 

        when 

Therefore, the only choice that isn't correct is 

 

Example Question #3 : Solving Trigonometric Equations And Inequalities

Find one possible value of .

Possible Answers:

Correct answer:

Explanation:

Begin by isolating the tangent side of the equation:

Next, take the inverse tangent of both sides:

Divide by five to get the final answer:

Example Question #4 : Solving Trigonometric Equations And Inequalities

Use trigonometric identities to solve for the angle value.

Possible Answers:

Correct answer:

Explanation:

There are two ways to solve this problem. The first involves two trigonometric identities:

The second method allows us to only use the first trigonometric identity:

Example Question #5 : Solving Trigonometric Equations And Inequalities

Use trigonometric identities to solve the equation for the angle value.

Possible Answers:

Correct answer:

Explanation:

The simplest way to solve this problem is using the double angle identity for cosine.

Substituting this value into the original equation gives us:

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