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tiffney
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Can anyone tell me the difference btween cos and sin, and tell me when creating waveform why the sin function creates a sawtooth appearance and the cos function does. Any help would be appreiciated. :!) :!)
mathwonk said:for a point on the unit circle, cos is the x coordinate and sin is the y coordinate. I.e. one is the shadow of the radius on the x-axis and the other the shadow of the radius on the y axis. Due to the symmetry of the circle as you go around the length of the shadow of the radius on the x-axis or on the y-axis look essentially the same, just out of phase.
Data said:Cosine is a phase shift of sine (and visa-versa). In other words,
[tex]\sin \theta = \cos \left(\theta - \frac{\pi}{2}\right)[/tex]
just a translation to the right by .
tiffney said:when creating waveform why the sin function creates a sawtooth appearance and the cos function does.
Both cos (cosine) and sin (sine) are trigonometric functions used in mathematics to calculate the relationship between the sides and angles of a triangle. The main difference between them is that cos calculates the ratio of the adjacent side to the hypotenuse, while sin calculates the ratio of the opposite side to the hypotenuse.
Cos and sin are related through the Pythagorean identity, which states that cos²θ + sin²θ = 1. This means that the square of the cosine of an angle plus the square of the sine of the same angle will always equal 1.
Yes, both cos and sin can be negative depending on the quadrant of the angle in which they are being evaluated. In the first and fourth quadrants, cos is positive and sin is negative. In the second and third quadrants, both cos and sin are negative.
The graph of cos is a curve that starts at 1 and decreases to -1 as the angle increases from 0 to 180 degrees. The graph of sin is a curve that starts at 0, increases to 1 at 90 degrees, decreases to 0 at 180 degrees, and then becomes negative as the angle increases further.
Cos and sin have numerous applications in real life, including in architecture, engineering, navigation, and physics. For example, cos is used in calculating the stability of structures, while sin is used in determining the trajectory of a projectile. They are also used in fields such as music, sound engineering, and animation for creating smooth curves and movements.