# Trig

Cos(2theta)=-1/2

There are 6 solutions, how do i solve this?

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asked by Thanh
1. cos (2Ø) = -1/2
we know cos 60° = + 1/2
and we know that 2Ø, our angle, must be in quadrants II or III by the CAST rule
so 2Ø = 180-60 = 120° or 2Ø = 180+60 = 240°
Ø = 60° or Ø = 120°

but the period of cos 2Ø is 180°
so adding 180° to our answers will produce more answers.
Ø = 60+180 = 240° or
Ø = 120+180 = 300°

so Ø= 60,120,240,300°

test by doubling any of these answers and taking the cosine on your calculator.

your statement that there are 6 solutions is not really correct, there is an infinite number of solutions, we can keep adding/subtracting 180 to any of our new answers to obtain more answers.

There are 6 solutions in the usual domain between 0° and 360°

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posted by Reiny

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