# Some trigonometric functions questions

• May 24th 2010, 04:22 PM
GAVREED2
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)
• May 24th 2010, 05:52 PM
pickslides
You may need to be a little more clearer with those proofs

Quote:

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
• May 24th 2010, 06:16 PM
GAVREED2
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....

Quote:

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

• May 24th 2010, 06:53 PM
harish21
Quote:

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

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

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

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

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

$\displaystyle \frac{1}{2sin^2x-1}$
• May 24th 2010, 07:10 PM
GAVREED2
Cheers!
Can't thank you enough mate......

Quote:

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

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

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

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

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

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