if cosx = 12/13 and x is a quadrant I angle. Find the value of sinx
make a sketch of the triangle
since cos x = 12/13, the adjacent is 12, the hypotenuse is 13 and by Pythagoras, the opposite side is 5
( 5^2 + 12^2 = 13^2 )
sin x = 5/13
To find the value of sin(x), we can use the Pythagorean Identity, which states that sin^2(x) + cos^2(x) = 1.
Given that cos(x) = 12/13, we can square both sides of the equation to get:
cos^2(x) = (12/13)^2
Simplifying, we have:
cos^2(x) = 144/169
Now, using the Pythagorean Identity, we can substitute this value into the formula:
sin^2(x) = 1 - cos^2(x)
sin^2(x) = 1 - 144/169
sin^2(x) = (169/169) - (144/169)
sin^2(x) = 25/169
Finally, taking the square root of both sides, we find:
sin(x) = sqrt(25/169)
sin(x) = 5/13
Therefore, the value of sin(x) is 5/13.