- Slides: 15
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. • 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
Now figure out where sin = -1/2 on the unit circle.
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 coterminal angle with the equivalent trigonometric ratio.
Where k is an integer and gives all the coterminal angles of the solution.
Practice • Solve the equation. Find the general solutions
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.
This is a difference of squares and can factor Solve each factor and you should end up with 4 solutions
Practice Find the general solutions for
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
Solve the following Replace cos 2 with 1 -sin 2
Solving for Multiple Angles • Multiple angle problems will now have a coefficient on the x, such as sin 2 x=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.
Find the general solutions for sin 3 x +2= 1