Trigonometric equations (1 Viewer)

[clintmyster]

I got these annoying questions for hw over the weekend from my teacher

I attempted them but i am a bit lost. Help would be much appreciated.

Cheers

 

[powerdrive]

Ok ive done all of them except 3.
Pretty sure theyre all right. Just check on 4 and 5, not sure if thats the only way to do them, but i cant think of any other way atm.

Tell me if you dont understand something.

 

[ssglain]

3. [The trick here is to view sinx and cosx each as a pronumeral, say, y and z. Then you can rewrite the equation as y² - 3yz - 4z² = 0 and factorise accordingly --> (y - 4z)(y + z) = 0]

sin²x - 3sinxcosx - 4cos²x = 0 (0 < x < 360)
(sinx - 4cosx)(sinx + cosx) = 0

sin x = 4cosx or sinx = - cosx
tan x = 4 or tan x = -1
x = 180n + tan<SUP>-1</SUP>(4) or x = 180n + tan<SUP>-1</SUP>(-1), where n = 0, 1, 2, ...

.: x = 76, 135, 256, 315 (to nearest degree)

 

[clintmyster]

Thanks for that guys. My teacher just gave us a few trig identities and expected us to solve those. I get the working out. That idea to rewrite the equation makes it look a lot more simpler!