Some trigonometric functions questions

May 2010
64
0
Palmy
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
angular velocity is 8 rad/s.

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)
 
Last edited:

pickslides

MHF Helper
Sep 2008
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Melbourne
You may need to be a little more clearer with those proofs

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
 
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May 2010
64
0
Palmy
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....

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
 
Feb 2010
1,036
386
Dirty South
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
angular velocity is 8 rad/s.

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

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

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

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

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

\(\displaystyle \frac{1}{2sin^2x-1}\)
 
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May 2010
64
0
Palmy
Cheers!

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

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

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

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

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

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

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