Further trigonometric equations (1 Viewer)

[Carl5]

Solve for 0° less than or equal to x less than or equal to 360°

2sin²x + 3cosx - 3 = 0

2sinxtanx - tanx + 2 sin x - 1 = 0

3cos²x - 7cosx + 4 = 0

I'm not sure about how to go about these...

 

[random-1005]

Solve for 0° less than or equal to x less than or equal to 360°

2sin²x + 3cosx - 3 = 0

2sinxtanx - tanx + 2 sin x - 1 = 0

3cos²x - 7cosx + 4 = 0

I'm not sure about how to go about these...

1st and 3rd are quadratics ( sin^2 +cos^2 =1) to rewrite number 1 in terms of cosx

for the second, rewrite tan as sin/cos

then multiply through by cos, and group in pairs

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

tanx=-1, sinx =1/2

 

[thongetsu]

1. change sin^2.x into cosx
(-2cosx - 1)(cosx - 1) = 0
solve. wasn't bothered.


2. what he said ^

3.(3cosx - 4)(cosx - 1) = 0

 

[hscishard]

The 2nd one doesn't require transforming tan into sin/cos

Just factorise straight from there.
tanx(2sinx-1) +1(2sinx-1)
(tanx+1)(2sinx-1)

 

[thongetsu]

oh lol, didnt see that

 

[Carl5]

Ok, it turns out I did go about them the right way but just didn't have confidence in myself. Though I still don't know what to do with the cosx = 4/3

By the way, thanks for the quick responses.

 

[Carl5]

Never mind. I realised that I'm not meant to do anything with it.

Thanks for the help