Warmup:
Find all solutions in the interval [0,2π).
1. 2sin2 x = 2 + cos x **Hint: use a Pythagorean Identity first**
Find all solutions.
2. 3cot2 x - 1 = 0
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Questions from HW?
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Look at the two equations below and describe how they are
different. We learned how to solve the first one, but how do
we solve the second?
Find all solutions in the interval [0,2π).
1.
cos x = √3
2
2.
cos 2x = √3
2
So what effect does the 2 have when placed in front of the x?
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Angles with a multiple in front of them!!!! Find all solutions in the interval [0,2π).
1. 2cos 3x ­ 1 = 0
2. 2sin 2x + √3 = 0.
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Finding all solutions with multiple angles!!!
Find all solutions.
1. tan 2x + √3 = 0
2. sec2 4x - 1 = 0
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There are times when the solutions to a trig. equation are
not on the unit circle and we need a calculator to help us
solve them.
Ex.) Find all the solutions to the following equations on [0,2π)
1.) 9cosx + 2 = 3
2.) sec2x + 0.5tanx = 1
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Classwork:
Find all solutions to the equation in the interval [0,2π).
1. sin 3x + 1 = 0
Find all solutions to the equation.
2. cos ½x = 3 cos ½x - 2
Find all solutions to the equation in the interval [0,2π).
3. 2 cos2 x - 1 = 0
4. 2 tan x cos x + 2 cos x = tan x + 1
Find all solutions to the equation.
5. 2 sin2 x - 5 sin x + 2 = 0
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Classwork (Answers):
Find all solutions to the equation in the interval [0,2π).
1. sin 3x + 1 = 0
x = π/2, 7π/6, or 11π/6
Find all solutions to the equation.
2. cos ½x = 3 cos ½x - 2
x = 4πn
Find all solutions to the equation in the interval [0,2π).
3. 2 cos2 x - 1 = 0
x = π/4, 3π/4, 5π/4 or 7π/4
4. 2 tan x cos x + 2 cos x = tan x + 1
x = 3π/4, 7π/4, π/3 or 5π/3
Find all solutions to the equation.
5. 2 sin2 x - 5 sin x + 2 = 0
x = π/6 + 2πn or 5π/6 + 2πn
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Homework
pg. 400
#17,18,22,24,34-36,44,45,54
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