Precalculus : Solve Trigonometric Equations and Inequalities in Quadratic Form

Example Questions

Example Question #1 : Solve Trigonometric Equations And Inequalities In Quadratic Form

If exists in the domain from , solve the following:       Explanation:

Factorize . Set both terms equal to zero and solve.   This value is not within the domain.   This is the only correct value in the domain.

Example Question #1 : Solving Trigonometric Equations And Inequalities

Solve for in the equation on the interval .      Explanation:

If you substitute you obtain a recognizable quadratic equation which can be solved for  .

Then we can plug back into our equation and use the unit circle to find that .

Example Question #1 : Solving Trigonometric Equations And Inequalities

Given that theta exists from , solve:       Explanation:

In order to solve appropriately, do not divide on both sides.  The effect will eliminate one of the roots of this trig function.

Substract from both sides. Factor the left side of the equation. Set each term equal to zero, and solve for theta with the restriction .       Example Question #4 : Solve Trigonometric Equations And Inequalities In Quadratic Form

Solve for   There is no solution. There is no solution.

Explanation:

By subtracting from both sides of the original equation, we get . We know that the square of a trigonometric identity cannot be negative, regardless of the input, so there can be no solution.

Example Question #5 : Solve Trigonometric Equations And Inequalities In Quadratic Form

Solve when   There are no solutions. There are no solutions.

Explanation:

Given that, for any input, , we know that , and so the equation can have no solutions.

Example Question #1 : Solve Trigonometric Equations And Inequalities In Quadratic Form

Solve when There are no solutions.    By adding one to both sides of the original equation, we get , and by taking the square root of both sides of this, we get From there, we get that, on the given interval, the only solutions are and . 