Trigonometric functions

Question

How to solve the following trigonometric function for x

 

sin(pi/4(x-6))= 0.5,     0<x<2pi

 

the answer is 1.33

 

thankyou

Answer 1

change the problem to cos(pi/4(x-6) = 0.5 and then the answer for x-6 is 4/3 = 1.33

cosA=.5 when A= pi/3 or 5pi/3 or -pi/3

A=pi/3 = (pi/4)(x-6)

x-6 = 4/3

(pi/4(4/3) = pi/3, but x = 6+4/3> 2pi disallowed by the problem

5pi/3 = (pi/4)(x-6)

5/3 = (x-6)/4

x-6 = 20/3

x=6+20/3 >2pi

-pi/3 = (pi/4)(x-6)

-1/3 =(x-6)/4

x-6 = -4/3

x= 6-4/3 = 4.66

same with keeping sine as the problem, there is no solution

sinA =.5

A = pi/6 or 5pi/6 (30 or 150 degrees)

A = pi/4(x-6) = pi/6

4(x-6) =6

x-6 =6/4 = 3/2

x= 3/2+6 = 15/2 = 7.5 but that's > 2pi

do the same setting A=5pi/6 for a 2nd solution

pi/4(x-6)=5pi/6

1/4(x-6) = 5/6

20(x-6)=6

x-6 =6/20 = 3/10

x=6.3 > 2pi = 2(3.14) = 6.28

unless you really meant (pi/4)(x-6) then

(pi/4)(x-6)=pi/6

(x-6)/4 = 1/6

x-6 = 2/3

x=2/3 +6 = 20/3 > 2pi

try A=5pi/6 = (pi/4(x-6)

5/6 = 1/4(x-6)

20(x-6) =6

x-6 = 6/20 = 3/10

x = 6.3>2pi

there is no solution

however you do the problem or interpret it, using sine, you can't get x<6 as that makes the angle negative and sine of a negative angle b will also be negative, not +1/2 and x can't be >2pi = about 6.28 that means if there were a solution it would have be 6<x<6.28