# Trig

posted by .

Cos(2theta)=-1/2

There are 6 solutions, how do i solve this?

• Trig -

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°
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°

## Similar Questions

1. ### trig

2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3π] So I need to find general solutions to solve the equation. But do I eliminate cos(x), like this... 2sin(x)cos(x)+cos(x)=0 2sin(x)cos(x)= -cos(x) 2sin(x) = …
2. ### trig

e.g. tan 315 = -1, does that work in our equation ?
3. ### trig

solve the equation of the domain 0¡Ü¦È¡Ü2¦Ð 3cos^2theta - 5costheta -1 = 3sin^2theta
4. ### Prove or Disprove

Cos(X+y)cos(x-y)= cos^2theta - sin^2theta I foiled the left side as a start because I can kind of see sin^2+cos^2=1 but I can't finish.
5. ### trig

given that 1/2pi<theta<pi and sin theta=1/5, use appropriate trigonometric formulas to find the exact values of the following (i) cos(2theta) (ii) cos theta (iii) sin(2theta)
6. ### Math

sin theta = 8/17 and theta is in the second quadrant. Find sin(2theta),cos(2theta),tan(2theta) exactly sin(2theta) cos(2theta) tan(2theta)
7. ### Math

sin theta = 8/17 and theta is in the second quadrant. Find sin(2theta),cos(2theta),tan(2theta) exactly sin(2theta) cos(2theta) tan(2theta) sin(2theta) would it be 2 x (8/17) cos(2theta) would be 2 x (15/17) tan(2theta) would be 2 x …
8. ### Precalc+trig

Solve tan(40/90) for the double angle cos(2theta). I know I use the x^2 + y^2 = r^2 formula and cos(2theta) = cos^2theta - sin^2theta. But I don't understand my answer
9. ### Precalc Trig

here's the question: solve for cos(2theta)=1 if you graph r= cos(2Theta) then graph r=1 you find that there are four places where the graphs intersect. however, when solved algebraically, there are two solutions which can be represented …
10. ### Trig

Solve each equation for exact solutions over the interval [0,360)where appropriate. Round approximate solutions to the nearest tenth degree. Sin^2Theta=Cos^2Theta+1 My Work: Using double angle Identity I subtract 1 to other side therefore: …

More Similar Questions