Trigonometry – Graphs & curvesThe Sine curve

• A sine wave is formed by plotting values of sine θ against θ.

• The base (x axis) is the angle θ and the equivalent sine values are obtained from tables of calculator.

• A simple sin plot illustrates the +/- quadrant relationship seen earlier

sin Angle (0 - 360)

-1.0

-0.5

0.0

0.5

1.0

0 60 120 180 240 300 360

Trigonometry – Graphs & curvesThe Sine curve

• In the first quadrant as θ increases from 0° to 90°, sin θ increases from 0 to 1

• In the second quadrant as θ increases from 90° to 180°, sin θ decreases from 1 to 0

• In the third quadrant as θ increases from 180° to 270°, sin θ decreases from 0 to -1

• In the fourth quadrant as θ increases from 270° to 360°, sin θ increases from -1 to 0

Trigonometry – Graphs & curvesThe Cosine curve

• A cosine wave is formed by plotting values of cos θ against θ.• The base (x axis) is the angle θ and the equivalent cos values are

obtained from tables of calculator.• A simple cos plot illustrates the +/- quadrant relationship seen

earliercos Angle (0 - 360)

-1.0

-0.5

0.0

0.5

1.0

0 60 120 180 240 300 360

Trigonometry – Graphs & curvesThe Cosine curve

• In the first quadrant as θ increases from 0° to 90°, cos θ decreases from 1 to 0

• In the second quadrant as θ increases from 90° to 180°, cos θ decreases from 0 to -1

• In the third quadrant as θ increases from 180° to 270°, cos θ increases from -1 to 0

• In the fourth quadrant as θ increases from 270° to 360°, cos θ increases from 0 to 1

Trigonometry – Graphs & curvesThe Tangent curve

• A tangent wave is formed by plotting values of tan θ against θ.

• The base (x axis) is the angle θ and the equivalent tan values are obtained from tables or calculator or the relationship :-

• tan θ = A simple tan plot illustrates the +/- quadrant relationship

seen earlier cos

sin

tan Angle (0 - 360)

-7.0

-5.0

-3.0

-1.0

1.0

3.0

5.0

7.0

0 90 180 270 360

Trigonometry – Graphs & curvesThe Tangent curve

• In the first quadrant as θ increases from 0° to 90°, tan θ increases from 0 to infinity

• In the second quadrant as θ increases from 90° to 180°, tan θ increases from minus infinity to 0

• In the third quadrant as θ increases from 180° to 270°, tan θ increases from 0 to infinity

• In the fourth quadrant as θ increases from 270° to 360°, tan θ increases from minus infinity to 0

Trigonometry – Angles in a quadrant

• When plotting the graphs present the data values in a table as below• Increase the number of data values to improve accuracy of plot

• Increase data points – for manual plot use 30° increments• For Msoft EXCEL use 10° increments (convert into Radians first)• Plot the three graphs as individual items with titles on each plot

Angle θ 0° 90° 180° 270° 360°

sin θ

cos θ

tan θ