Trigonometry Graphs

To sketch the trigonometry graphs of the functions – Sine, Cosine and Tangent we need to know the period, phase, amplitude, and maximum and minimum turning points. These graphs are used in many areas of engineering and science. Few of the examples are the growth of animals and plants, engines and waves, we have graphs for all the trigonometric functions

The graphical representation of sine, cosine and tangent functions are explained here briefly with the help of the corresponding graph. Students can learn from here and practice questions based on it.

Graphs of Trigonometric Functions

Sine, Cosine and tangent are the three important trigonometry ratios, based on which functions are defined. Below are the graphs of the three trigonometry functions. Sin a, Cos a, and Tan a. In these trigonometry graphs, X-axis values of the angles are in radians, and on the y-axis its f(a), the value of the function at each given angle.

Sin Graph

  • b = sin a
  • The roots or zeros of b = sin a is at the multiples of Π .
  • The sin graph passes the x-axis as sin a = 0 there.
Max value of Graph Min value of the graph
1 at  π/2 -1  at 3 (π/2)

Sine Graph

The height of the curve at each point A line value of Sine
Sin theta period Π / 2

Cos Graph

  • b = Cos a
  • b = cos a graph’s is the graph we get after shifting b= sin a  π/2 units to the left.
  • As sin (a +  π/2 ) = cos a
Max value of Graph Min value of the graph
1 at 0, 4π -1  at 2π

Cosine Graph

There are a few similarities between the sine and cosine graphs as follows:

  1. Both have the same curve which is shifted along the x-axis.
  2. Both have an amplitude of 1.
  3. Have a period of 360°

Sin and Cos Graph

Tan Graph

The tan function is completely different from sin and cos function. The function here goes between negative and positive infinity, crossing through 0 over a period of π radian.

 

Tan Graph

  • b = tan a
  • The tangent graph has an undefined amplitude as the curve tends to infinity.
  • It also has a period of 180°

Graphing Trig Functions Practice

Let’s practice what we learned in the above paragraphs with few of trigonometry functions graphing practice.

1) Sketch the graph of y = 5 sin 2x°  + 4

  • amplitude = 5, so the distance between the max and min value is 8.
  • number of waves = 2(Each wave has a period of 360° ÷ 2 = 180°)
  • moved up by 4 (since c > 0)
  • max turning point when (5 × 1)+ 4= 7 and min turning point when (5 × -1) + 4 = -1
  • The graph looks like:

The six trigonometric functions are

  1. Sine
  2. Cosine
  3. Tangent
  4. Cosecant
  5. Secant
  6. Cotangent.

Graphs of Trigonometric Functions

Trigonometric graphs for these Trigonometry functions can be drawn if you know the following:

Amplitude –

  • It is the absolute value of any number multiplied with it on the trigonometric function.
  • The height from the center line to the peak (or trough) is called amplitude.
  • You can also measure the height from highest to lowest points and then dividing it by 2.
  • It basically tells how tall or short the curve is.
  • Also, notice the minus on it depending on the function is in usual orientation or upside down.

Period

The Period goes from any point (one peak ) to the next matching point.

Phase

How far the function is shifted from the usual position horizontally is called Phase shift.

  • Max and min turning points.

The above terms are also important to use the graph of trigonometry formulas.

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