Question

Solve each equation for 0 = x = 2π :

i) 2cos^(2)x + 3cosx – 2 = 0
ii) sinx = sqrt 3cosx

(Rewards for correct answer)

Answer 1

did you mean
\[
(1)\quad2cos^2x+3cosx−2=0\\
(2)\quad \sin x=\sqrt{3}\cos x\\

\text{for }0\le x \le2\pi\]
???

Answer 2

a. (2cosx-1)(cosx+2)=0

cosx=1/2 or cosx=-2

x={π/3, 5π/6}

This is correct, i promise...

Answer 3

If you set p=cos x in the first one, you get: 2p²+3p-2=0.
You can solve this, using the quadratic formula.
Once you've got you p, remember cos x = p, so solve for x.

Answer 4

Do you get mines @jahvoan

Answer 5

i got the answer but what is the corresponding angle for -2 on the unit circle?

Answer 6

There isn't. cosx=-2 has no solutions, because the x-coordinate of a point on the unit circle (which is the cosine) only has values from -1 to 1...

Answer 7

ok thanks

Answer 8

solve equation 2

Answer 9

You can divide both sides by cos x and remember sinx/cosx = tan x

Answer 10

but on the right it is sqrt cosx

Answer 11

No, it's sqrt(3) * cosx

Answer 12

no look at the problem up top

Answer 13

It says: sinx = sqrt 3cosx

This can only mean:\[ \sin x = \sqrt{3} \cdot \cos x\]So dividing by cos x gives:\[\frac{ \sin x }{\cos x }=\sqrt{3} \Leftrightarrow \tan x=\sqrt{3}\]And this is a "nice" value of tan x.

If you interpret it otherwise, you can't solve it...

Answer 14

so what will be the answer for sqrt 3 on the unit circle?

Answer 15

Remember that special triangle with sides of a, 2a and a√3?

Answer 16

is it pi/6

Answer 17

no its pi/3 right or wrong?

Answer 18

60 degrees, or pi/3

Answer 19

thanks mayne

Answer 20

why is equation 2 not considered to be an identity?

Answer 21

Identities hold for every x.
This one is only true if x = pi/3.

Identity: sinx=cos(pi/2-x). No matter what x is, it's always true!