Question

Solve the following equations for all solutions of x

2sin^2x+3cos-3=0

Answer 1

u need to convert sin^2 x into cos^2 x
which i dentity u know of, does this ?

Answer 2

an identity relating sin^2 x and cos^2 x is ?

Answer 3

Pythagorean?

Answer 4

yes, state that or find sin^2 x from that, what u get ?

Answer 5

sin^2x+cos^2x=1

Answer 6

yes so sin^2 x from ^ will be ?

Answer 7

1+cos^2x

Answer 8

sin^2x+cos^2x=1
so
sin^2 x = 1-cos^2 x
got this ??

Answer 9

Oh...yeah, yeah, yeah

Answer 10

now put that in 2sin^2x+3cos-3=0
and u get an equation only in terms of cos x

Answer 11

2cos^2x+3cos-1=0?

Answer 12

2sin^2x+3cos-3=0
2-2cos^2x +3cos x -3 = 0
-2cos^2 x + 3cos x -1 = 0
2cos^2 x -3cos x +1 = 0
got this ?

Answer 13

Yes...now I have 2cos^x-3cosx+1=0

Answer 14

now put cos x =y
so u get a quadratic in y
can u solve quadratic equations ?

Answer 15

Just with a=2,b=-3,c=1?

Answer 16

yes :) so u know the formula ?

Answer 17

Yeah

Answer 18

So is there going to be two answers then?

Answer 19

what 2 answers u got ?

Answer 20

I came up with x=3+-sqrt72/4

Answer 21

Unsure though...

Answer 22

72? b^2-4ac = (-3)^2 - 4(2)(1) = 9-8 = ?

Answer 23

Ugh....I multiplied x4ac
So...9-8=1

Answer 24

yes, so two values of y are >?

Answer 25

Is it 3+-1/4?

Answer 26

so 2 values are ?

Answer 27

13/4,11/4?

Answer 28

13 ? 11 ?
(3+1)/4 or (3-1) /4
so, 4/4 or 2/4
so, 1 or 1/2
ok?

Answer 29

OMG...sorry. I was taking 3+1/4
It's all over 4, yes

Answer 30

so u have cos x =1 or cos x = 1/2
right ? can u solve this 2 equations ?

Answer 31

So cosign of 1 is pi/2

Answer 32

And pi/6?

Answer 33

cos (0) = 1
cos (pi)= 1
so cos x =1 will give x= 0,pi,2pi,....n*pi

Answer 34

Thank you so much for your time. These processes are very hard for me. I know practice will help. Thank you again for walking me through each step.

Answer 35

still cos x =1/2 is remaining

Answer 36

So if cosx=1/2 then @ pi/3?

Answer 37

yes, and other values ?

Answer 38

Also 5pi/3 @ 300deg

Answer 39

Thank goodness for a unit circle :)

Answer 40

yeah, in general, it will be pi/3 + 2n*pi
x= pi/3 , pi/3+ 2pi, pi/3 + 4pi, ...pi/3 + 2n*pi