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Find the domain of the function y = 5∕3 tan(3∕4x).

A)  All real numbers except odd integer multiples of 2π∕3
B)  All real numbers except odd integer multiples of 4π∕3
C)  All real numbers except 0 and odd integer multiples of 2π∕3
D)  All real numbers except 0 and odd integer multiples of 4π∕3���

Sagot :

Answer:

A

Step-by-step explanation:

tan(3x/4)=sin(3x/4)/cos(3x/4)

So the domain of tah(3x/4) is all real numbers except real numbers that make cos(3x/4)=0.

cos(pi/2 +n pi)=0

So we need to solve 3x/4=pi/2+n pi

Multiply both sides by 4/3: x=4/3(pi/2+n pi)

Distribute: x=2pi/3+4n pi/3

Or x=(2pi+4 n pi)/3

Or x=2 pi/3 ×(1+2n)

So odd integer multiples of 2pi/3 is the numbers to be excluded from the domain.

The required domain of the function y = 5/3 tan(3/4x) is  (-∞, ∞) - {- 2/3 (2n + 1)π, 2/3 (2n + 1)π}.

What are trigonometric equations?

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.

y = 5/3 tan(3/4x)
Function tan defined at every x except x = nπ/2 where n = odd number. i.e x = (-∞,∞) - {(2n+1) * π/2, -(2n+1) * π/2}

3/4 * x = (2n + 1 ) * π/2
x = (2n + 1) * 4/3* π/2
x = 2/3 (2n + 1)π
So the required domain for the given function y = 5/36tan(3/4)x is given as,
Domain (x) = (-∞, ∞) - {- 2/3 (2n + 1)π, 2/3 (2n + 1)π}.

Thus, the required domain of the function y = 5/3 tan(3/4x) is  (-∞, ∞) - {- 2/3 (2n + 1)π, 2/3 (2n + 1)π}.

Learn more about trigonometry equations here:

brainly.com/question/22624805

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