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Solving Trigonometric Equations

Solving Trigonometric Equations. First Degree Trigonometric Equations:. These are equations where there is one kind of trig function in the equation and that function is raised to the first power. Steps for Solving:. Isolate the Trigonometric function.

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Solving Trigonometric Equations

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  1. Solving Trigonometric Equations

  2. First Degree Trigonometric Equations: • These are equations where there is one kind of trig function in the equation and that function is raised to the first power.

  3. Steps for Solving: • Isolate the Trigonometric function. • Use exact values to solve and put answers in terms of radians. • If the answer is not an exact value, then use inverse functions on your calculator to get answers

  4. Now figure out where sin = -1/2 on the unit circle.

  5. Complete the List of Solutions: • If you are not restricted to a specific interval and are asked to give the general solutions then remember that adding on any integer multiple of 2π represents a co-terminal angle with the equivalent trigonometric ratio.

  6. Where k is an integer and gives all the coterminal angles of the solution.

  7. Practice • Solve the equation. Find the general solutions

  8. Second Degree Trigonometric Equations: • These are equations that have one kind of Trigonometric function that is squared in the problem. • We treat these like quadratic equations and attempt to factor or we can use the quadratic formula.

  9. This is a difference of squares and can factor Solve each factor and you should end up with 4 solutions

  10. Practice Find the general solutions for

  11. Writing in terms of 1 trig fnc • If there is more than one trig function involved in the problem, then use your identities. • Replace one of the trig functions with an identity so there is only one trig function being used

  12. Solve the following Replace cos2 with 1-sin2

  13. Solving for Multiple Angles • Multiple angle problems will now have a coefficient on the x, such as sin2x=1 • Solve the same way as previous problems, but divide answers by the coefficient • For general solutions divide 2 by the coefficient for sin and cos. Divide by the coefficient for tan and cot.

  14. Find the general solutions for sin 3x +2= 1

  15. Practice

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