[InadequateJusticex]

Need some tips on how to start off these questions...really stuck
Solve:

[tehforum]

Use sin^2+cos^2 =1

Rearrange to get sin in terms of cos.

Sub it into the first equation.

[mazboy008]

Basically these are quadratic equations in either sinx or cosx. You also may have to used the identity: (sinx)^2 + (cosx)^2 = 1

Useful Website:
Click show steps for solution:
http://www.wolframalpha.com/input/?i...+2sin%5E2theta
http://www.wolframalpha.com/input/?i...%5E2theta+%3D0

[f1mad]

First one:

cos^2x+sin^2x=1

So 2cos^2x+2sin^2x=2 -> re-arrange this to get this in terms of 2sin^2x=... something, such that the original equation will now be in terms of cos.

Second one:

3sin^2x- 4cos^2x= sinxcosx

Divide both sides by sinxcosx, and get it into quadratic form in terms of tanx.

[TLK]

(Original post by InadequateJusticex)
Need some tips on how to start off these questions...really stuck
Solve:

For the first one you use the trig identity:


For the second one divide by and replace the sin/cos with tan

[InadequateJusticex]

(Original post by tehforum)
Use sin^2+cos^2 =1

Rearrange to get sin in terms of cos.

Sub it into the first equation.

I did:


But I dunno if that's right? :/

[TLK]

(Original post by InadequateJusticex)
I did:


But I dunno if that's right? :/

3-3costheta=2(1-cos^2theta)
3-3costheta=2-2cos^2theta
2cos^2theta - 3costheta +1 = 0
Factorise to get your values.

[InadequateJusticex]

(Original post by f1mad)
First one:

cos^2x+sin^2x=1

So 2cos^2x+2sin^2x=2 -> re-arrange this to get this in terms of 2sin^2x=... something, such that the original equation will now be in terms of cos.

Second one:

3sin^2x- 4cos^2x= sinxcosx

Divide both sides by sinxcosx, and get it into quadratic form in terms of tanx.

Sorry...can you illustrate that? I don't know how sinx divided by sinxcosx would make tanx? :s


And what is the difference between sinx and sin theta?

[f1mad]

(Original post by InadequateJusticex)
Sorry...can you illustrate that? I don't know how sinx divided by sinxcosx would make tanx? :s


And what is the difference between sinx and sin theta?

I used sinx instead of sintheta for convenience.

E.g. 3sin^2x/ sinxcosx= 3sinx(sinx)/(sinx)cosx = 3sinx/cosx = 3tanx.

[InadequateJusticex]

(Original post by f1mad)
I used sinx instead of sintheta for convenience.

E.g. 3sin^2x/ sinxcosx= 3sinx(sinx)/(sinx)cosx = 3sinx/cosx = 3tanx.

Oh tyvm but does sinx mean the same thing as sin theta? Like how you can write dy/dx or f'(x)?

[Llewellyn]

(Original post by InadequateJusticex)
Oh tyvm but does sinx mean the same thing as sin theta? Like how you can write dy/dx or f'(x)?

No, it's not an alternative. The only way to write sine of x is sinx. Theta is only used a lot in angles out of convention.

Sinx = sin theta if x = theta.