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GRAPHING
PACKAGE
240 Trigonometric functions (Chapter 9)
Discussion
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² Discuss how to find thex-intercepts of y= tanx.
² How can we simplify tan(x¡¼)?
² How many solutions does the equation tanx=2have?EXERCISE 9D
1 Sketchthe following functions for ¡¼ 6 x 6 ¼:
a y= 2 tanx b y= tan 3x c y= tanx+2
d y= 3 tan 2x e y= 2 tanx¡ 1 f y= 2 tan 3x+2
Use technology to check your answers.2
a period^23 ¼and principal axis y=2 b period¼ 2 and principal axis y=¡ 3.3 Findpandqgiven the following graph of the function y= tanpt+q.Activity
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Click on the icon to run a card game for trigonometric functions.Linear equations such as 2 x+3 = 11 have exactly one solution. Quadratic equations of the form
ax^2 +bx+c=0, a 6 =0 have at most two real solutions.Trigonometric equationsgenerally have infinitely many solutions unless a restricted domain such as
06 x 63 ¼ is given.For example, suppose that Andrew in theOpening Problemwants to know when the green light will be
16 metres above the ground. To find out, he will need to solve a trigonometric equation. If the wheel
keeps rotating, the equation would have infinitely many solutions. Andrew may therefore specify that he is
interested in thefirsttime the green light is 16 metres above the ground.E Trigonometric equations
Findbandcgiven that the function y= tanbx+c, b> 0 , has:cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_09\240CamAdd_09.cdr Wednesday, 15 January 2014 10:41:13 AM BRIAN