# Trigonometry

Find all the angles θ in the interval [-2pi, 2pi] for which cos(3θ) = 1/sqrt(2)

I'm not sure why I would have to look for angles in 3 revolutions of the circle (3 positive, 3 negative).

Also how would I convert cos(3θ) = 1/sqrt(2) to a radian value? Do I just need to know the unit circle by heart?

1. 👍 0
2. 👎 0
3. 👁 112
1. You should know, or by use of your calculator, that cos(±45°) = 1/√2
so 3θ = ±45° and θ = ±15°
now the period of cos(3θ) is 360°/3 or 120°
±15, ±135, ±255, ±105, ±225, and ±345

in radians, you know that π/6 = 30°
so 15° = π/12
to quickly convert the above degrees to radians I do the following steps
135/15 = 9
then 135° = 9(π/12) = 3π/4
±π/12, ±3π/4, ±17π/12, ±7π/12, ±5π/4, and ±23π/12

Proof:
www.wolframalpha.com/input/?i=plot+y+%3D+cos(3x)+,+y+%3D+1%2F%E2%88%9A2+from+-2%CF%80+to+2%CF%80

1. 👍 0
2. 👎 0
2. The above post was my me, forgot to put in my name

1. 👍 0
2. 👎 0
posted by Reiny
3. Page 2 of the following has a nice unit circle,
have it handy

tutorial.math.lamar.edu/pdf/trig_cheat_sheet_reduced.pdf

1. 👍 0
2. 👎 0
posted by Reiny
4. Thanks. I'm not permitted to use a calculator, which makes this a lot harder.

1. 👍 0
2. 👎 0
posted by Pat

## Similar Questions

1. ### Algebra 2

Find the values of the inverse function in radians. sin^-1(0.65) a. 0.71+2pi n and -0.71+2pi n b. 0.71+2pi n and -3.85+2pi n c. 0.86+2pi n and -0.86 +2pi n d. -0.61+2pi n and 2.54+2pi n 2. tan^-1(0.09) a.-0.09+2pi n b. no such

2. ### Math

Can I please get some help on these questions: 1. How many solutions does the equation,2sin^2 2 θ = sin2θ have on the interval [0, 2pi]? 4? ...what about 4cos2θ = 8cos^2 2θ? 2. True or False: sin^2 4x = 1 has 8 solutions on

asked by mysterychicken on June 2, 2013
3. ### Calculus help??

I'm not sure how to solve this and help would be great! d/dx [definite integral from 0 to x of (2pi*u) du] is: a. 0 b. 1/2pi sin x c. sin(2pi x) d. cos (2pi x) e. 2pi cos (2pi x) This is the fundamental theorem, right? What's

asked by ashley on April 28, 2015
4. ### Calc

Find the exact total of the areas bounded by the following functions: f(x) = sinx g(x) = cosx x = 0 x = 2pi I set my calculator to graph on the x-axis as a 2pi scale. The two functions appear to cross three times between x = 0 and

asked by Sarah on April 21, 2007
5. ### Algebra2

Find the values of the inverse function in radians. 1. sin^-1(0.65)? answer choices: a. 0.71+2pi n and -0.71+2pi n b. 0.71+2pi n and -3.85+2pi n c. 0.86+2pi n and -0.86 +2pi n d. -0.61+2pi n and 2.54+2pi n My answer is B

asked by Steve on May 2, 2017
6. ### math

find all solution to the equation 3 cos(x+4)=1. in the interval of 0

asked by alicia otto on March 26, 2016
7. ### Trig

Find all solutions of the equation in the interval [0,2pi) 2 cos^2 x-cos x = 0 -2cos^2 + cosx + 0 (x+1/2) (x+0/2) (2x+1) (x+0) -1/2,0 2Pi/3, 4pi/3, pi/2, 3pi/2 my teacher circled pi/2 and 3pi/2 What did I do wrong? I don't

asked by Anonymous on April 10, 2017
8. ### Math

For questions 2 and 3, use a calculator to find the values of the inverse function in radians. sin^-1(0.65) 0.71 + 2pi n and –0.71 + 2 pi n 0.71 + 2 pi n and –3.85 + 2 pi n 0.86 + 2pi n and –0.86 + 2pi n –0.61 + 2pi n and

asked by Harry on June 16, 2018
9. ### calc

i did this problem and it isn't working out, so i think i'm either making a dumb mistake or misunderstanding what it's asking. A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is

asked by jane on April 2, 2009
10. ### Calculus AP - Volume of Revolution

Hi. I have a few calculus problems that I have to do using the washers and shell method to find out what the volume of the graph rotated is. I'll post one question at a time with my work. The problem is, I should be getting the

asked by Kira on March 5, 2007