# Some trigonometric functions questions

#### 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)

Last edited:

#### pickslides

MHF Helper
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

• GAVREED2

#### 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....

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

#### harish21

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

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

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

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

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

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

• GAVREED2

#### GAVREED2

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

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

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

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

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

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