Question

simple trig identities problem!

Solve the following quadratic trig equations algebraically (without graphing technology) for the domain 0o < x < 360o. Use exact solutions whenever possible.

a) 6cos^2(theta ) + cos(theta ) - 1 = 0

b) 2 - 2sin^2( theta) = cos(theta )

Answer 1

put cos(theta) = x in the first equation and solve for x, and then substitute it back into cos theta

Answer 2

for the second one 2-2sin^theta = 2(1-sin^2theta) = 2 cos^2theta and then put cos theta = x and solve for x

Answer 3

i'm sorry but i don't understand any of that...

Answer 4

substitute cos theta = x in the first problem and post what you got.

Answer 5

as in.. 6x^2+x-1??
like a quadratic?

Answer 6

yes.

Answer 7

so solve that quadratic equation.

Answer 8

i dont remember how to when the x^2 value has a coefficient..

Answer 9

Find out and solve it. If you have done it before, I am sure you can solve it.

Answer 10

http://www.youtube.com/watch?v=1Pva-Iv43Nc

Answer 11

well everything becomes a fraction if i factor out the 6....
that vid didnt help.

Answer 12

6x2+x-1 = 6x2+3x-2x-1

Answer 13

alright, so now what is the next step?

Answer 14

do you know how to factor quadratic equations?

Answer 15

using the qudratic frmula? yes. why did i need to break up that middle term?

Answer 16

okay. there is another way to solve quadratic eqns. its called factoring.
so 6x2+3x-2x-1 = 3x(2x+1)-1(2x+1) = (3x-1)(2x+1)=0. so x = 1/3 or x = -1/2.

Answer 17

ok, but how does this relate to the trig question? haha

Answer 18

so if x = 1/3, it means cos theta = 1/3. and x= -1/2. so cos theta = -1/2. solve foe theta within 0 and 360 degrees

Answer 19

wwhat do you mean by solving for theta between 0 and 360?
sorry i'm so bad at this!

Answer 20

just find theta.

Answer 21

dont worry about the 0 and 360.

Answer 22

post the values of theta you got.

Answer 23

arent the x= values the solutions?

Answer 24

No, x is just a variable you used to denote cos theta. so you have to find theta