Presentacion sobre funcoines trigonometricas

Trigonometria

1. Trigonometric functions To graph f(x) = sin x To graph g(x) = cos x To see h(x) = tan x

2. Graphing f(x) = sin x x 0° 90° 180° 270 360 f(x) Period = 2pi Amplitude

3. Graphing f(x) = cos x x 0° 90° 180° 270 360 f(x) Period = 2pi Amplitude

4. Graphing f(x) = tan x

5. Example

6. Investigation: What happen to f(x) = sin x when:

7. Parameters in the sine and cosine functions Amplitude Number of periods in 360° Horizontal translation Vertical translation Amplitude Number of periods in 360° Horizontal translation Vertical translation Period = 360°/ b

8. Exercises Draw in your GDC the graph y = 2sinx , for 0° <x < 360° and solve the equation 2sinx = 1.2 Draw in your GDC the graph y = 2cosx + 1 , for 0° <x < 360° and solve the equation 2cosx + 1 = 2 Draw in your GDC the graph f(x) = sinx and g( x)= cosx , for 0° <x < 360° and solve the equation sinx = cosx Find the amplitude and period of the following functions: f(x) = 4 sinx , g(x) = -2cos (3x) , h(x) =5 sin Give the amplitude and period of the following functions and write the function: 360° 360°

9. Match each equation with one of the sketch graphs which follow.

10. Sketching Sketch the graph for : f(x) = - sinx Sketch the graph for : g(x) = - cosx Sketch the graph for : h(x) = - 2sinx Sketch the graph for : y = 3cosx Sketch the graph for : y = - sin(2x) Find the amplitude and period of the following functions: y= -2 sinx , y= 3cosx and y = -sin (2x)