![Lesson 5 Trig. functions 2013 (1).notebook
October 29, 2013
Sine function
period
amplitude
maximum value = 1
minimum value = -1
amplitude= 1
range= [-1,1]
period= 2π ( or 360o)
Ene 1009:53 a.m.
4](https://image.slidesharecdn.com/trigonometricfunctions-131029065926-phpapp02/85/IB-SL-Trigonometric-functions-4-320.jpg)
![Lesson 5 Trig. functions 2013 (1).notebook
October 29, 2013
Cosine function
period
amplitude
maximum value = 1
minimum value = -1
amplitude= 1
range= [-1,1]
period= 2π ( or 360o)
Ene 1009:53 a.m.
6](https://image.slidesharecdn.com/trigonometricfunctions-131029065926-phpapp02/85/IB-SL-Trigonometric-functions-6-320.jpg)
![Lesson 5 Trig. functions 2013 (1).notebook
October 29, 2013
Transformations of the trigonometric functions
in [2π, 2π]
y = sin x + 2
y = sin (x + 2)
y = sin (2x)
y =2 sin x
y = sin (x)
y = sin x
Ene 1009:53 a.m.
9](https://image.slidesharecdn.com/trigonometricfunctions-131029065926-phpapp02/85/IB-SL-Trigonometric-functions-9-320.jpg)
![Lesson 5 Trig. functions 2013 (1).notebook
October 29, 2013
Combined transformations
y= a sin [b(x c)]+ d
vertical translation
horizontal translation
horizontal dilation: period =
amplitude= |a| (vertical dilation)
Transformations sine.ggb
the same applies for cosine function
Ene 1009:53 a.m.
18](https://image.slidesharecdn.com/trigonometricfunctions-131029065926-phpapp02/85/IB-SL-Trigonometric-functions-18-320.jpg)
![Lesson 5 Trig. functions 2013 (1).notebook
October 29, 2013
Combined transformations
y= a tan [b(x c)]+ d
vertical translation
horizontal translation
horizontal dilation: period =
amplitude= |a|
Ene 1009:53 a.m.
19](https://image.slidesharecdn.com/trigonometricfunctions-131029065926-phpapp02/85/IB-SL-Trigonometric-functions-19-320.jpg)
IB SL Trigonometric functions
- 1. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Trigonometric Functions Revisited • Recognise the graphs of sine, cosine and tangent functions, their periods and amplitudes. • Revise the geometrical transformations of trigonometric functions. • Draw sketches of the trigonometric functions. Ene 1009:53 a.m. 1
- 4. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Sine function period amplitude maximum value = 1 minimum value = -1 amplitude= 1 range= [-1,1] period= 2π ( or 360o) Ene 1009:53 a.m. 4
- 6. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Cosine function period amplitude maximum value = 1 minimum value = -1 amplitude= 1 range= [-1,1] period= 2π ( or 360o) Ene 1009:53 a.m. 6
- 8. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Tangent function period vertical asymptotes: x = π/2 , x = 3π/2, x = 5π/2,.... period : π no amplitude Ene 1009:53 a.m. 8
- 9. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Transformations of the trigonometric functions in [2π, 2π] y = sin x + 2 y = sin (x + 2) y = sin (2x) y =2 sin x y = sin (x) y = sin x Ene 1009:53 a.m. 9
- 10. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Vertical translations y = sin x +2 y = sin x y = sin x 1 y = sin x + c y = cos x + c represent vertical translations of vector y = tan x + c period and amplitude don't change Ene 1009:53 a.m. 10
- 11. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Horizontal translations y = sin x y = cos x period and amplitude don't change Ene 1009:53 a.m. 11
- 12. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Horizontal translations y = sin ( x ±a ) y = cos ( x ±a ) y = tan ( x ±a ) represent horizontal translations of the curves y = sinx, y = cos x and y = tan x y = sin ( x - a ) to the right y = sin ( x + a ) to the left Ene 1009:53 a.m. 12
- 13. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Vertical dilation (stretch) y =2 cos x y = cos x y = sin x y = a sin x y = a cos x are dilations of the curves y = cos x y = a tan x y = tan x parallel to the y-axis the amplitude changes to |a| Ene 1009:53 a.m. 13
- 14. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Horizontal dilation (stretch) y = sin x y = sin (2x) period : π horizontal stretch , scale factor ½ period changes to half the original Ene 1009:53 a.m. 14
- 15. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 period= 6 π y = sin x period= 2 π horizontal stretch , scale factor 3 period changes to three times the original Ene 1009:53 a.m. 15
- 16. Lesson 5 Trig. functions 2013 (1).notebook y = sin (bx) are dilations of the curves y = cos(b x) October 29, 2013 y = sin x y = cos x parallel to the x-axis the period changes to y = tan( bx) is a dilation of the curve y = tan x parallel to the x-axis the period changes to Ene 1009:53 a.m. 16
- 17. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Reflections reflection in the x-axis y = sin x y = sin x y = tan(x) y = tan x reflection in the y-axis period and amplitude don't change Ene 1009:53 a.m. 17
- 18. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Combined transformations y= a sin [b(x c)]+ d vertical translation horizontal translation horizontal dilation: period = amplitude= |a| (vertical dilation) Transformations sine.ggb the same applies for cosine function Ene 1009:53 a.m. 18
- 21. Lesson 5 Trig. functions 2013 (1).notebook October 29, 2013 Book Ex 8D 8 E Other related websites you can visit http://members.shaw.ca/ron.blond/sc.APPLET/index.html http://www.ies.co.jp/math/products/trig/applets/graphSinX/graphSinX.html http://magnuskarlsson.nu/mathplets/trig/trigfunc.html http://www.mathsnet.net/asa2/modules/p13unitcircle3.html <http://207.207.4.198/pub/flash/15/graphing.swf> Ene 1009:53 a.m. 21