Trigonometry – Graphs & curves The 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

Trigonometry – Graphs & curves The 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 & curves The 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 earlier

Trigonometry – Graphs & curves The 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 & curves The 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

Trigonometry – Graphs & curves The 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