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14.714.7
Solving Trig EquationsSolving Trig Equations
Find all solutions of for the interval0 < 360.
Original equation
Solve for 0.
Distributive Property
Divide each side by –1.
Simplify.
Factor.
Example:
Now use the Zero Product Property.
Answer: The solutions are 30°, 150°, and 270°.
or
Find all solutions of for the interval 0 < 2.
Original equation
Solve for 0.
Factor
Example:
Use the Zero Product Property.
Answer: The solutions are
or
Find all solutions of each equation for the given interval.
a.
b.
Answer:
Answer:
More problems:
Solve for all values of ifis measured in radians.
Original equation
Subtract
Factor.
or Zero Product Property
Solve.
Example:
Look at the graph of to find solutions of
The solutions are and so on, and
so on.
The only solution in the interval 0 to are and
The period of the sine function is radians. So the
solutions can be written as and
where k is any integer.
Similarly, the solutions for
Answer: The solutions are
and
Solve for all values of if ismeasured in degrees.
Original equation
Solve for 0.
Factor.
Example:
Solve for in the interval of
or
Answer: The solutions are
a. Solve for all values of if ismeasured in radians.
b. Solve for all values of if ismeasured in degrees.
Answer:
Answer:
There is more:
Solve
Original equation
Multiply.
Factor.
Example:
or
Thus, is not a solution.
is undefined.
Answer: The solution is
Check
Solve
Answer: The solution is .
Your turn:
Solve
Subtract 1 and addto each side.
Original equation
Multiply each side by 4.
Factor.
Example:
or
is undefined for
Answer: The solutions areand
Solve
Answer:
Your turn again: