What is the value of x?sin(x+22)°=cos(2x−7)°Remember to show all of you work for credit!Given cosx=1213 and sinx=513 . What is ratio for tan x ?leave answer as a fraction in simplest formRemember to show all of you work for credit!
Accepted Solution
A:
Q1: Given sin(x+22)° = cos(2x−7)° Using the concept of Right triangles and Trigonometric ratios, we can use a formula given as follows :- If, sin(A) = cos(B). Then we must have A + B = 90 degrees. We have sin(x+22)° = cos(2x−7)°Then it must be true that (x+22)° + (2x−7)° = 90 degrees.(x + 22) + (2x - 7) = 90 3x + 15 = 90 3x + 15 - 15 = 90 - 15 3x = 75 [tex] \frac{3x}{3} =\frac{75}{3} \\\\x = 25 \;degrees [/tex]Hence, x = 25 degrees is the final answer. Q2: Given cos(x) = 1213 and sin(x) = 513. It says to find ratio of tan(x).Using the concepts of Trigonometric ratios, We can the formula that relates all three functions i.e. sin(x), cos(x), and tan(x).tan(x) = [tex] \frac{sin(x)}{cos(x)} [/tex]We can plug the given values in the formula.[tex] tan(x) = \frac{513}{1213} [/tex] is the final answer.