Domain and Range of trigonometric functions - LPM4U 04

Trigonometric Functions - Domain and Range of trigonometric functions - LPM4U 04

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Video have 2 parts.

PART 01 OF VIDEO:

Domain and Range of trigonometric functions - LPM4U 04

PART 02 VIDEO:

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Summary theory:

Domain and Range of trigonometric functions

All trigonometric functions are basically the trigonometric ratios of any given angle. For example if we take the functions, f(x)=sin x, f(z) = tan z , etc, we are considering these trigonometric ratios as functions. Since they are considered to be functions, they will have some domain and range

-1 ≤sin x ≤1

-1 ≤cos x ≤1

Trigonometric Functions

So, the domain of f(x) = tan x  will be R – (2n+1)π2  and the range will be set of all real numbers, R. We know that sec x, cosec x and cot x are the reciprocal of cos x, sin x and tan x respectively. Thus,

sec x = 1/cosx

cosec x = 1/sinx

cot x = 1/tanx

Example: Find the domain and range of y = cos(x) – 3

Solution:

Domain: x ∈ R

Range: - 4 ≤ y ≤ - 2, y ∈ R

Notice that the range is simply shifted down 3 units.

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Note:

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AUG 2019