Graphing Trigonometric Functions

The Sine Function Angle Sine Angle Sine 90 180 270 360 Angle Sine 90 1 180 270 -1 360 Angle Sine 90 180 270 360

Angle Sine 180 30 0.5 210 – 0.5 45 0.707 225 – 0.707 60 0.866 240 – 0.866 90 1 270 –1 120 300 135 315 150 330 – 0.5 90 180 270 360 90 360 270 180 y = sin x

Angle Cosine The Cosine Function 1 180 –1 30 0.866 210 – 0.866 45 0.707 225 – 0.707 60 0.5 240 – 0.5 90 270 120 300 135 315 150 330 The Cosine Function 90 360 270 180 90 360 270 180 y = cos x

{y| -1 y 1} {all real numbers} Range Domain 1 360° 90 360 270 180 1 -1 y = sin x {y| -1 y 1} {all real numbers} Period Amplitude Range Domain 1 360°

{y| -1 y 1} {all real numbers} Domain Range 1 360° 90 360 270 180 1 y = cos x -1 {y| -1 y 1} {all real numbers} Domain Range Period Amplitude 1 360°

For the graph of Amplitude = Period =

To Graph a Trigonometric function don’t make a table Just depend on its parent function and the transformations, so far; amplitude and period

y = 2sin x y = sin x y = sin x Amplitude = 2 period = 360° 2 90 360 270 180 -1 1 90 360 270 180 -1 1 y = sin x period = 360° -2

y = cos x y = 3 cos x y = 3cos 2x Amplitude = 3 period = 180° 3 3 90 270 180 360 1 -1 90 270 180 360 1 -1 90 270 180 360 1 -1 -3 -3 period = 180°

The Tangent Function Asymptotes Amplitude undefined period = 180° 90 270 360 period = 180°