Solver

Are you trying to compute this is MATLAB? and you would have to supply the value of b.

usually diff(a,b) implies a-b.

Time period of a signal is the time it requires to come back to its starting/original position after completing one cycle. There are two fundamental ways to calulating the time period of a signal or any system.

First, you could look at the waveform on a 2D graph with x-axis as the time axis and y-axis as the amplitude axis. So if the signal starts at zero and is a sinusoidal signal, then its time period would be when if crosses zero three time. 

Second, Like Hazeem mentioned, Time period is the inverse of the frequency, which physically makes sense as frequency is the number of occurances/repetations (How many times does it repeats) of a signal in unit time, hence we can take the reciprocal.

The best way to approach this problem is to think about the polar form representation. So a complete circle is 2PI. In your case 

you have to find the tan inverse of the given value and then add 2PI to the angle value you obtain. 

use the identity \(cos(x) = sin(90-x)\)

Hence we can write this as

\(k(x) = 5sin(3\pi/4 - 2x) -3\)

So the parent function basically means the simplest mathematical equation to represent a curve. 

In this case its a sine curve. Now if you were to replace x with 2x, physically you are increasing the frequrency of the curve and by using the scalar -3 you are scaling and limiting it to the amplitude range of +3 and -3 instead of -1 to 1. This basically implies that the form remains the same in all cases as they all belong to the same family of cosine curves. 

for better understanding: 

http://fooplot.com/

Plot your cosine functions to see the change!

The missing number is 53. 

\(4{sin}^{2}(x) =3\)

\(x= {sin}^{-1}(\sqrt{3} \div 2) \)

using standard value tables for sine

\(x= 60 deg\)

\(y = cos(x) \)

The parent function is the simplest form of the given function with the same degree.

Solution:

Since x and y are complementary they add up to 90degrees or PI/2 rads. 

\(x+y = 90 \rightarrow (1)\)

rearranging the terms we get:

 \(y= 90-x\)

Taking the sin on both sides we get the following identity:

\(sin(y) = sin(90-x) \)

\(\Rightarrow sin(90)cos(x) - cos(90)sin(x)\)

\(\Rightarrow (1)(cos(x)) - (0)(sin(x)) \)

\(\Rightarrow cos(x)\)

\(\Rightarrow -0.3\)

\(Answer: sin(y) = -0.3\)