Graphs of Trigonometry Functions

In this lesson, we will look at the graphs of the trigonometry functions: sine, cosine and tangent.

Properties Of The Sine Graph

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 θ 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

• 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˚.

Properties Of The Tangent Graph

• The 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˚.

The following video will explain more about the properties of the sine graph, cosine graph and tangent graph. You may want to look at the lesson on unit circle, if you need revision on the unit circle definition of the trigonometry functions..

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