Question

Help solving for each equation for 0 (equal or less than) x ( equal or less than) 2pi:?

a) 2cos^2 x + 3cosx – 2 = 0

b) sinx = cos2x

c) sin x = sqrt3 cos x

d) Explain why the trig equation in part (c) is not an identity?

Answer 1

[0,360] is the interval for all 4 problems?

Answer 2

@SolomonZelman what do you mean interval?

Answer 3

For the first equation, let cosx = y, then you have the equation 2y^2 + 3y - 2 = 0. Can you solve this quadratic equation by factoring it?

Answer 4

@navk Can you please help me solve it? I just started the topic today

Answer 5

@rcatabijan you mean factoring quadratic equations or solving trigonometric equations? or Both?

Answer 6

@navk both

Answer 7

for problem a. let cos(x)=v v^2+3v-2 =0 and use quadratic formula.

for problem b. 1) square both sides, apply sin^2x+cos^2x=1 and solve...

Answer 8

do for c, what you do for b

Answer 9

@SolomonZelman can you please provide me with an example?

Answer 10

I am going to do b and you do c. deal ?

Answer 11

@SolomonZelman okay deal, i'll solve for c. but please give me a detail on the steps for b please so I can apply the knowledge on c?

Answer 12

\(\Large\color{orangered}{ \bf sinx = cos(2x) }\)
\(\Large\color{orangered}{ \bf sinx = cos(x+x) }\)
\(\Large\color{orangered}{ \bf sinx = cos(x)cos(x)-sin(x)sin(x) }\)
\(\Large\color{orangered}{ \bf sinx = cos^2(x)-sin^2(x) }\)
\(\Large\color{orangered}{ \bf sinx = 1-sin^2(x)-sin^2(x) }\)
\(\Large\color{orangered}{ \bf sinx = 1-2sin^2(x) }\)
\(\Large\color{orangered}{ \bf 1-2sin^2(x)-sin(x) =0 }\)
\(\Large\color{orangered}{ \bf -2sin^2(x)-sin(x)+1 =0 }\)
\(\Large\color{orangered}{ \bf 2sin^2(x)+sin(x)-1 =0 }\)

solve the quadratic saying sin(x)=a

Answer 13

@SolomonZelman

(2sinx - 1)(sinx + 1) = 0

sinx = 1/2 .....sinx = - 1

x = π/6 , 5π/6 ....x = 3π/2

I did the question using my teachers examples, is it wrong?

Answer 14

good work. I didn't notice it's factorable. otherwise I would never have offered quadratic, i hate it:)

Answer 15

Can you do C ?

Answer 16

Thanks @SolomonZelman :) Umm, I can try but can you help me like you did with b?

Answer 17

\(\Large\color{purple}{ \bf sin(x)=\sqrt{3}cos(x) }\)

1) Divide both sides by cos(x)
2) Use tan(x) = sin(x)/cos(x)

Answer 18

@SolomonZelman

sinx/cosx = √3

tanx = √3

x = π/3 , 4π/3

How about this one?

Answer 19

yes, I think it looks good

Answer 20

I am sure you know why C is not an identity. Saying you know that C is not true for all x values.

Answer 21

equation in part (c) is not an identity because C is not a true for all x values right @SolomonZelman ?

Answer 22

yeah:)

Answer 23

and do you need help with a ?

Answer 24

Woohoo! Yes please @SolomonZelman

Answer 25

\[2\cos^2(x) + 3\cos(x) – 2 = 0 \]\[(2\cos~x-1)(\cos~x+2)=0\]yu can finish a from here

Answer 26

@SolomonZelman cosx = 1/2

x = π/3 , 5π/3

Answer 27

yes and the other option is cos(x)=-2

Answer 28

Thanks @SolomonZelman :D