Simple trig. (#4) (1 Viewer)

[sinophile]

Solve for 0<=x<=360:
2sin^2(theta)+cos^2(theta)=2

I can't seem to isolate this equation into only one type of ratio. Am I supposed to isolate it to one ratio? What the hell do I do?

 

[kurt.physics]

Solve for 0<=x<=360:
2sin^2(theta)+cos^2(theta)=2

I can't seem to isolate this equation into only one type of ratio. Am I supposed to isolate it to one ratio? What the hell do I do?

Notice how 2sin²(theta) + cos²(theta) is like sin²(theta) + cos²(theta)?

And we know that sin²(theta) + cos²(theta) equals 1.

So we can try to work around this, factoring wont works, but if you see

2sin²(theta) + cos²(theta) = 1 + 1

2sin²(theta) = 1 + 1 - cos²(theta)

2sin²(theta) - 1 = 1 - cos²(theta)

And from rearranging sin²(theta) + cos²(theta) = 1, we have

sin²(theta) = 1 - cos²(theta)

this is the RHS of the equation 2sin²(theta) - 1 = 1 - cos²(theta),

So making the substitution,

2sin²(theta) - 1 = sin²(theta)

2sin²(theta) - sin²(theta) = 1

sin²(theta) = 1

therefore

(sin(theta))² = 1

sin(theta) = +1 and -1 (from the root)

So then you just have to solve that equation for 0<= x <= 360.

If you need any help, just ask.

Goodluck!

 

[shady145]

2sin^2 theta + cos^2theta=2
cos^2theta = 1-sin^2theta (from trig identities)
now sub it in
2sin^2theta-sin^2theta+1=2
sin^2theta=1
root both sides. now it is in all quadrants coz root gives + and -
theta = 90, 180, 270, 360

 

[shady145]

whoops i meant only 90 and 270

 

[sinophile]

SORRY!

The question is actually:
Solve for 0<=x<=360:
2sin^2(theta)+cos(theta)=2

(Cos is not squared) Can someone please explain how to get the answer please?

 

[jet]

2sin^2x + cosx = 2.

Im letting x=theta.

We use the same identity as before:
sin^2(x)=1-cos^2(x)
Now we sub it in:
2 - 2cos^2(x) + cosx = 2
And, rearranging it we have
2cos^2(x)-cosx = 0
cos(x)[2cos(x)-1]=0
cos(x) = 0 or cos(x) = 1/2
Hence x= 90,270, 60, 300

 

[h3ll h0und]

are u getting these questions from preliiminary cambridge textbook? these questions look very familiar.... lol xD