SOLUTION: The function f(x) = 4 - 3sinx is defined for the domain 0 ≤ x ≤ 2π i) Solve the equation f(x) = 2 ii) Sketch the graph of y = f(x) iii) Find the set of values of k for wh

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Question 1202355: The function f(x) = 4 - 3sinx is defined for the domain 0 ≤ x ≤ 2π
i) Solve the equation f(x) = 2
ii) Sketch the graph of y = f(x)
iii) Find the set of values of k for which the equation f(x) = k has no solution
The function g(x) = 4 - 3sinx is defined for the domain π/2 ≤ x ≤ A
(iv)State the largest value of A for which g has an inverse
(v) For this value of A, find the value of g^-1(3)
Answer by math_tutor2020(3816) (Show Source):
You can put this solution on YOUR website!

I'll do the first three parts to get you started.

Part (i)

f(x) = 4 - 3*sin(x)
4 - 3*sin(x) = f(x)
4 - 3*sin(x) = 2
-3*sin(x) = 2-4
-3*sin(x) = -2
sin(x) = -2/(-3)
sin(x) = 2/3
x = arcsin(2/3) or x = pi - arcsin(2/3)
x = 0.729728 or x = 2.411865
Those values are approximate.
Make sure your calculator is in radian mode.
Arcsine is another way of saying inverse sine.

Answers: Approximately x = 0.729728 and x = 2.411865

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Part (ii)

Graph

Focus on the portion on the interval
2pi = 6.28 approximately

The interactive Desmos graph is shown here
https://www.desmos.com/calculator/lmsl75jor0
The blue shaded area represents the interval

You can use GeoGebra as another alternative.

If you prefer to use a TI83 or TI84, then let me know if you need me to go over the steps for graphing.

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Part (iii)

According to the graph in part (ii), the min and max are y = 1 and y = 7 respectively.

If , then f(x) = k will have at least one solution.
Otherwise, there are no solutions.

Answer: If k < 1 or k > 7, then there are no solutions.