Graph sine, cosine and tangent functions – Lesson
Graph of Sine Function
The sine function is a periodic function that maps an angle to a value between -1 and 1. The graph of the sine function forms a wave-like pattern that repeats itself after a certain interval (2π radians or 360 degrees).
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The Graph of sin(x) has 1. Maximum value = 1, and the Minimum value = -1. 2. The amplitude of sine curve =1 3. Periodic behavior with a period of 2π radian or 360 degrees. 4. The graph passes through (0,0) and 5. The graph has a vertical symmetry about the x-axis. |
G
raph of Sine in Degrees
Sine Radian
Graph of Cosine Function
The cosine function is also a periodic function, similar to the sine function. It maps an angle to a value between -1 and 1.
The graph of the cosine function forms a wave-like pattern that repeats itself after a certain interval (2π radians or 360 degrees).
The cosine function has the same frequency as the sine function, but it is phase shifted by π/2 radians (or 90 degrees). This means that at t=0, the cosine function starts at its maximum value, while the sine function starts at zero.
The amplitude (height) of the cosine wave is determined by the coefficient in front of the cosine function.
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The Graph of cos(x) has 1. Maximum value = 1, and the Minimum value = -1. 2. The amplitude of cos curve =1 3. Periodic behavior with a period of 2π radian or 360 degrees. 4. The graph passes through (0,0) and 5. The graph has a vertical symmetry about the x-axis. |
Graph of Cosine in Degrees
Graph of the Cosine funciton in Radian
Graph of Tangent Function
The tangent function maps an angle to a value that represents the ratio of the opposite side to the adjacent side of a right triangle. The graph of the tangent function is periodic, with a period of 2π radians (or 360 degrees), and has asymptotes at every odd multiple of π/2 radians (or 90 degrees), where the function becomes undefined. The graph of the tangent function forms a wave-like pattern that alternates between positive and negative values, approaching the asymptotes but never reaching them. The amplitude (height) of the wave is determined by the coefficient in front of the tangent function and the frequency (number of complete cycles per unit interval) is determined by the argument in the tangent function.
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Since \(y=\tan x=\frac{\sin x}{\cos x}\) is undefined when \(\cos x=0 \). Therefore the graph of tan(x) has vertical asymptotes at \(x=\frac{\pi}{2}+k \pi, k \in \mathbb{Z}\) For the general tangent function where :
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Graph of tangent in Degrees