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...

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

Conclusion:

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