Question

What is the value of x?

sin(x+11)°=cos(2x+22)°

Enter your answer in the box.
x =

Answer 1

x = 19

2 x 19 = 38 + 22 = 60
19 + 11 = 30

30 + 60 = 90

Answer 2

General Idea:

`Sin (A) = Cos(90 - A)`

Given:

`sin(x+11)^(\circ)=cos(2x+22)^(\circ) \Rightarrow 1^(st) \; equation`

Applying the concept:

Using the given rule we can rewrite the left hand side of the equation as below:

`Sin(x+11)=cos(90 - (x+11))=cos(90 -x-11)=cos(79-x)`

Substituting the above result in 1st equation, we get...

`cos(79-x)=cos(2x+22)\\\\Equating \; angles\; we get...\\\\79-x=2x+22\\Adding \; x \; on \; both \; sides \; and \; subtracting \; 22 \; on \; both \; sides, \; we \; get...\\\\79 -22 = 2x + x\\ Combining \; like \; terms \\\\3x = 57\\ Dividing \; by \; 3 \; on \; both \; sides \\\\ (3x)/(3) = (57)/(3) \\Simplifying \; fraction \; on \; both \; sides\\\\x=19`

Conclusion:

The value of x which will make the equation sin(x+11)°=cos(2x+22)° TRUE is 19 degrees.