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Example Question #1 : Solving Trigonometric Equations And Inequalities
Use trigonometric identities to solve the following equation for :
Use the trigonometric identities to switch sec into terms of tan:
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
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
Replacing our substitution therefore gives
Within our designated domain, we get three answers between our two equations.
Therefore, the only choice that isn't correct is
Example Question #3 : Solving Trigonometric Equations And Inequalities
Find one possible value of .
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.
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.
The simplest way to solve this problem is using the double angle identity for cosine.
Substituting this value into the original equation gives us: