Period and Range of Trigonometric Functions

Write out the following questions and use the applet below to find the period and range of:
1 (a) sin(x) (b) cos(x) (c) tan(x)
2 (a) sin(2x) (b) cos(3x) (c) tan(4x)
3 (a) 5sin(x/2) (b) 4cos(x/3) (c) 5tan(x/4)
(The answers are at the bottom of the page. When you're finished, try making up your own questions.)

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Answers:
1 (a) sin(x) has a period of 2π and a range of [-1, 1]
(b) cos(x) has a period of 2π and a range of [-1, 1]
(c) tan(x) has a period of π and an infinite range.

2 (a) sin(2x) has a period of π and a range of [-1, 1]
(b) cos(3x) has a period of 2π/3 and a range of [-1, 1]
(c) tan(4x) has a period of π/4 and an infinite range.

3 (a) 5sin(x/2) has a period of 4π and a range of [-5, 5]
(b) 4cos(x/3) has a period of 6π and a range of [-4, 4]
(c) 5tan(x4) has a period of 4π and an infinite range.

T. Healy, Created with GeoGebra