Friday

February 12, 2016
Posted by **Nada** on Saturday, July 24, 2010 at 4:36pm.

- Trig -
**Reiny**, Saturday, July 24, 2010 at 5:47pmset 2cos(3x) - 1 = 0

2cos(3x) = 1

cos 3x = 1/2

I will use degrees, we can always switch to radians later

3x = 60° or 3x = 300° by the CAST rule

x = 20° or x = 100°

the period of cos 3x = 360/3 or 120°

so by adding/subtracting 120° to any of our answers we can produce as many new answers as we want,

so for 0 ≤ x ≤ 360°

x = 20°, 140°,100° , 220° , 260°, 340°

or in radians

x = π/9, 7π/9, 5π/9, 11π/9 , 13π/9, 17π/9

- Trig -
**Nada**, Saturday, July 24, 2010 at 6:02pmOk so how did you get x to equal 20, 140,100........

And I also don't get where 3x=60 or 100 came from, can you please explain these parts by showing the math? Thank you

- Trig -
**Reiny**, Saturday, July 24, 2010 at 6:09pmI knew, or my calculator told me, that

cos 60° = 1/2 or cos 300° = 1/2

so 3x had to be 60° or 3x had to be 300°

well if 3x = 60 , what is x? (divide both sides by 3)

same for 3x = 300

x = 100

(on your calc.

enter

2nd

cos

.5

=

you should get 60 )

- Trig -
**Nada**, Saturday, July 24, 2010 at 9:34pmSrry I keep asking questions, but I noticed that you left out the negative sign on the 2 when you set the equation to zero, was that a mistake or were you suppose to do it like that?