Sine Wave Vs Cosine Wave Math

Cosine follows the opposite pattern.

Sine wave vs cosine wave math. Cosine is just like sine but it starts at 1 and heads down until π radians 180 and then heads up again. Notice how at 0 radians the sine wave is at the bottom of the graph zero and the cosine wave is at the extreme of the graph 1. Or to the left we may use interchangeably recall the trigonometric identity cos 90 x sin. The relationship between the cosine and sine graphs is that the cosine is the same as the sine only it s shifted to the left by 90 degrees or π 2.

The pressure of a pure tone is mapped by a sine wave but sound is not a sine wave. Plot of sine and cosine in fact sine and cosine are like good friends. The other commonly used angles are 30 45 60 and their respective multiples. You can also see graphs of sine cosine and tangent.

The trigonometry equation that represents this relationship is look at the graphs of the sine and cosine functions on the same coordinate axes as shown in the following figure. It is known as sine wave as it has the similar shape as the sine function when it is plotted on a graph. It is the rapid oscillation of air pressure. A sine wave depicts a reoccurring change or motion.

And play with a spring that makes a sine wave. Therefore they are related. To complete the picture there are 3 other functions where we divide one side by another but they are not so commonly used. This is because sine and cosine are cofunctions described later.

There s a small tweak. They follow each other exactly π 2 radians 90 apart. We have just shifted the sine graph by π 2 radians to the right. Sine that starts at the max is called cosine and it s just a version of sine like a horizontal line is a version of a vertical line.

As can be seen from the figure sine has a value of 0 at 0 and a value of 1 at 90. This time we start at the max and fall towards the midpoint. A cosinewave is said to be sinusoidal because cos x sin x π 2 displaystyle cos x sin x pi 2 which is also a sine wave with a phase shift of π 2 radians. They are equal to 1 divided by cos 1 divided by sin and 1 divided by tan.

Normally sine starts the cycle at the neutral midpoint and races to the max. The graph shows the repetition of one wave segment in a repeated manner.