The function f : x → 4 − 3 sin x is deﬁned for the domain 0 ≤ x ≤ 2π.
(i) Solve the equation f(x) = 2. [3]
(ii) Sketch the graph of y = f(x). [2]
(iii) Find the set of values of k for which the equation f(x) = k has no solution.
The function g : x → 4 − 3 sin x is deﬁned for the domain 1
2
π ≤ 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

Question

The function f : x  → 4 − 3 sin x is deﬁned for the domain 0 ≤ x ≤ 2π.
(i) Solve the equation f(x) = 2. [3]
(ii) Sketch the graph of y = f(x). [2]
(iii) Find the set of values of k for which the equation f(x) = k has no solution. 
The function g : x  → 4 − 3 sin x is deﬁned for the domain 1
2
π ≤ 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

cwrw238 · Answer

4 - 3 sin x = 2
3sin x = 2
sin x = 0.6667
use you calculator to find the value of x in the first quadrant
another value will be in second quadrant