Math 30-1
Trigonometric Equations: Lessons #1-2
Solving Trigonometric Equations
Objective: By the end of this lesson, you will be able to:
In a trigonometric equation, the variable is the ___________.
Solving Trig Equations by Graphing
We can find approximate solutions to trig equations by using a graphing calculator. There are two ways to do this:
Method 1:
· Enter Y1 =
Y2 =
· The solutions are
Method 2:
· Move all terms to ________ ___________ so that the equation = _______.
· Enter Y1 =
· The solutions are
e.g. 1) Use both methods to solve the equation in radians. How many solutions are there? Round to the nearest hundredth.
Make sure you pay attention to the given domain.
e.g. 2) Solve to the nearest degree for .
Some trig equations have an infinite number of solutions. If this is the case, you may be asked to give a general solution, rather than the solutions over a given domain. To do this:
· Find the approximate solutions over ________ _____________ of the function.
· Add ___________________ of the _____________ to the solutions.
e.g. 3) Give the general solution to in radians, to the nearest hundredth.
e.g. 4) Is it possible to have a trig equation that has no solution? If so, give an example.
Solving Trig Equations Algebraically
To solve trigonometric equations algebraically, remember:
· Special Triangles
· CAST Rule
· To find the general solution:
* Please give answers as exact values whenever possible. *
e.g. 5) Solve the equation ,
A trigonometric equation can also have a degree higher than 1. If the equation has degree 2:
1. You will probably need to ______________ the equation
You can factor the same way you factor quadratic equations – just think of the trig ratio (e.g. ) as the variable:
2. Then set each factor equal to ______ and solve each equation.
e.g. 6) Solve the following trig equations:
a) , general solution in radians
b) ,
c) ,
d) , general solution to the nearest degree
e.g. 7) April tried to solve the equation , , as follows:
Step 1:
Step 2:
Step 3:
Step 4:
Identify and correct April’s mistake.
Assignment: Handout p. 577-582 #5-7, 9-13, MC 1-2
p. 211-214 #3, 5 (give general solution), 7, 9-11, 16-17
For a challenge: #18, 21-22