Trigonometry – Graphs & curves The Sine curve A sine wave is formed by plotting values of sine θ...
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Transcript of Trigonometry – Graphs & curves The Sine curve A sine wave is formed by plotting values of sine θ...
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