Part 1)
sin(x+22)°=cos(2x−7)°
we know that
the sine and cosine are co-functions
So
sin (theta) = cos (90 - theta)------> This implies that the angles sum to 90°
therefore
( x + 22) + (2x - 7) = 90 simplify
3x + 15 = 90 subtract 15 from both sides
3x = 75 divide both sides by 3
x = 25
The answer Part 1) is x=25°
Part 2) Given cos x=12/13 and sin x =5/13
What is ratio for tanx ?
we know that
tan x = sinx / cos x
tan x = (5/13) / (12/13) = (5/13) * (13/12) = 5/12
the answer Part 2) is 5/12
