Find-domain-of-function-r-x-arc-cos-3-4-2sin-x-

Question Number 122337 by benjo_mathlover last updated on 15/Nov/20

F i n d d o m a i n o f f u n c t i o n

r (x) = arc \cos (\frac{3}{4 + 2 \sin x})

Commented by liberty last updated on 16/Nov/20

The function defined for values of x

for which - 1 ⩽ \frac{3}{4 + 2 \sin x} ⩽ 1 .

Since 4 + 2 \sin x > 0 at any x, the problem

is reduced to solving inequality

\frac{3}{4 + 2 \sin x} ⩽ 1, whence 3 ⩽ 4 + 2 \sin x

i . e \sin x ⩾ - \frac{1}{2} \Rightarrow - \frac{π}{6} + 2 k π ⩽ x ⩽ \frac{7 π}{6} + 2 k π

for k ϵ Z . ▴

Commented by benjo_mathlover last updated on 16/Nov/20

Commented by benjo_mathlover last updated on 16/Nov/20

c o r r e c t . . t h a n k s