# Thread: Some trigonometric functions questions

1. ## Some trigonometric functions questions

Help needed on these also. Either solved or information to help me solve them myself would be vcery helpful. thanks a million.......

1)Prove that:

A) cosx/1-sinx - cosx/1+sinx = 2tanx

B) sinx/sinx+cosx + cosx/sinx-cosx = 1/2sin^2x-1

2) a) State the amplitude (A) the period(T) and the frequency(F) for
the periodic function 120 sin(100pi t)V.

b) Through how many degrees does a wheel rotate in 10ms if its

c) Sketch one cycle of the given function showing the values of
each variable where the curve crosses the axis.
V=50sin(4.2*10^2t)

2. You may need to be a little more clearer with those proofs

Originally Posted by GAVREED2

2) a) State the amplitude (A) the period(T) and the frequency(F) for
the periodic function 120 sin(100pi t)V.
For the function $\displaystyle y=a\sin bx$

The amplitude is $\displaystyle a$, the period can be found by $\displaystyle \frac{2\pi}{b}$

Have a read of this Trigonometric Functions

3. ## Amended proofs

Thanks so much for your input it was very helpful. i read the functions info and things are starting to become clearer. I also changed the format of the proofs if you could have a look that would be great....

Originally Posted by pickslides
You may need to be a little more clearer with those proofs

For the function $\displaystyle y=a\sin bx$

The amplitude is $\displaystyle a$, the period can be found by $\displaystyle \frac{2\pi}{b}$

Have a read of this Trigonometric Functions

4. Originally Posted by GAVREED2
Help needed on these also. Either solved or information to help me solve them myself would be vcery helpful. thanks a million.......

1)Prove that:

A) cosx/1-sinx - cosx/1+sinx = 2tanx

B) sinx/sinx+cosx + cosx/sinx-cosx = 1/2sin^2x-1

2) a) State the amplitude (A) the period(T) and the frequency(F) for
the periodic function 120 sin(100pi t)V.

b) Through how many degrees does a wheel rotate in 10ms if its

c) Sketch one cycle of the given function showing the values of
each variable where the curve crosses the axis.
V=50sin(4.2*10^2t)
A) cosx/1-sinx - cosx/1+sinx = 2tanx

$\displaystyle \frac{cosx}{1-sinx} - \frac{cosx}{1+sinx}$

$\displaystyle = \frac{cosx(1+sinx) - cosx(1-sinx)}{1-sin^{2}x}$...simplifying this gives you 2tanx

----------------------------------------------------------
B) sinx/sinx+cosx + cosx/sinx-cosx = 1/2sin^2x-1

$\displaystyle \frac{sinx}{sinx+cosx} + \frac{cosx}{sinx-cosx}$

$\displaystyle \frac{sinx(sinx-cosx) + cosx(sinx+cosx)}{(sinx+cosx)(sinx-cosx)}$

$\displaystyle \frac{sin^2x - sinx.cosx + sinx.cosx +cos^2x}{sin^2x-cos^2x}$

$\displaystyle \frac{1}{sin^2x-(1-sin^2x)}$

$\displaystyle \frac{1}{2sin^2x-1}$

5. ## Cheers!

Can't thank you enough mate......

Originally Posted by harish21
A) cosx/1-sinx - cosx/1+sinx = 2tanx

$\displaystyle \frac{cosx}{1-sinx} - \frac{cosx}{1+sinx}$

$\displaystyle = \frac{cosx(1+sinx) - cosx(1-sinx)}{1-sin^{2}x}$...simplifying this gives you 2tanx

----------------------------------------------------------
B) sinx/sinx+cosx + cosx/sinx-cosx = 1/2sin^2x-1

$\displaystyle \frac{sinx}{sinx+cosx} + \frac{cosx}{sinx-cosx}$

$\displaystyle \frac{sinx(sinx-cosx) + cosx(sinx+cosx)}{(sinx+cosx)(sinx-cosx)}$

$\displaystyle \frac{sin^2x - sinx.cosx + sinx.cosx +cos^2x}{sin^2x-cos^2x}$

$\displaystyle \frac{1}{sin^2x-(1-sin^2x)}$

$\displaystyle \frac{1}{2sin^2x-1}$