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Trigonometric Graphs
Lessons On Trigonometry
Trigonometric Functions

Properties Of The Sine Graph

sine graph in degrees

  • The sine function forms a wave that starts from the origin.
  • sin θ = 0 when θ = 0˚, 180˚, 360˚, …
  • Maximum value of sin θ is 1 when θ = 90 ˚. Minimum value of sin θ is –1
    when θ = 270 ˚. So, the range of values of sin θ is –1 ≤ sin θ ≤ 1.
  • As the point P moves round the unit circle in either the clockwise or anticlockwise
    direction, the sine curve above repeats itself for every interval of 360˚. The interval over which
    the sine wave repeats itself is called the period.

Properties Of The Cosine Graph

cosine graph in degrees

  • The cosine function forms a wave that starts from the point (0,1)
  • cos θ = 0 when θ = 90˚, 270˚, …
  • Maximum value of cos θ is 1 when θ = 0˚, 360˚. Minimum value of cos θ
    is –1 when θ = 180 ˚. So, the range of values of cos θ is – 1 ≤
    cos θ ≤ 1.
  • As the point P moves round the unit circle in either the clockwise or anticlockwise
    direction, the cosine curve above repeats itself for every interval of 360˚. Its period is 360˚.
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Properties Of The Tangent Graph

tangent graph in degrees

  • The tangent curve is not continuous. It breaks at θ = 90˚ and 270˚, where the function
    is undefined.
  • tan θ = 0 when θ = 0˚, 180˚, 360˚.
  • tan θ = 1 when θ = 45˚ and 225˚.
  • tan θ = –1 when θ = 135˚ and 315˚.
  • tan θ does not have any maximum or minimum values. The range of values of tan θ
    is – ∞ < tan θ < ∞
  • As the point P moves round the unit circle in either the clockwise or anticlockwise
    direction, the tangent curve above repeats itself for every interval of 180˚. Its period is 180˚.
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Properties of the sine graph, cosine graph and tangent graph
You may want to look at the lesson on unit of measurement lap, if you need rewrite on the unit circle definition of the trigonometric functions .
Graphs of the trig functions
A demonstration of the sine graph, cosine graph and tangent graph .
How to Graph the Sine and Cosine Functions?
Graph the Sine and Cosine functions on the coordinate plane using the unit traffic circle.
Determine the knowledge domain and range of the sine and cosine functions.
Determine the period of the sine and cosine functions.

Graph the Tangent function and identify key properties of the function
Graph the Tangent function on the coordinate plane using the unit of measurement circle.
Determine the sphere and range of the Tangent function.
Determine the period of the Tangent serve .
Graphs of transformed sin and cos functions
This lesson shows examples of graphing transformed y = drop the ball x and y = colorado x graph ( including changes in period, amplitude, and both vertical & horizontal translations ). There is besides an model of how to graph yttrium = tan ten using the yttrium = sin x and y = cosine x functions .
Examples:

  1. Graph y = 3sin2x
  2. Graph y = 4cos 1/2 x – 2
  3. Graph y = -3sin4(x – π/6) + 1
  4. Graph y = tan x
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Try the free Mathway calculator and problem problem solver below to practice respective mathematics topics. Try the given examples, or type in your own problem and check your answer with the bit-by-bit explanations.
Mathway Calculator Widget

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