# Math Help - Find all answers given the following

1. ## Find all answers given the following

for the following domain

The steps that I used:
cos(x+3) =1/5
x+3 = cos-1 (1/5)
x= cos-1(1/5) -3
that gives me one of the answers

for this cos-1(0.7)= x
this gave me one of the answers

How do I find the other answers

2. Originally Posted by midnightwynter
for the following domain

The steps that I used:
cos(x+3) =1/5
x+3 = cos-1 (1/5)
x= cos-1(1/5) -3
that gives me one of the answers

for this cos-1(0.7)= x
this gave me one of the answers

How do I find the other answers
HI

$5\cos (x+3)=1$

$\cos (x+3)=\frac{1}{5}$

cos is positive here so it must be in the first and fourth quadrant .

x+3= 78.46 , 281.54

x= 75.46 , 278.54 (in degrees)

x= 1.317 , 4.861 (in radians)

(b) $\cos x=0.7$

again cos is positive (1st and 4th quadrant)

x=0.795 , 5.488 , 7.078 , 11.77 (in radians)

There are 2 extra solutions (red) because the domain goes up to 4 pi , which means another round . So just add 2pi to 0.795 and 5.488 respectively to get them .