the hypotenuse is the radius of the circle and the length of the hypotenuse is always equal to 1.
x is the adjacent side of your angle and y is the opposite side of your angle.
by pythagorus, adjacent side squared plus opposite side squared = hypotenuse squared.
since adjacent side = x and opposite side = y and hypotenuse = 1, pythagorus equation becomes:
x^2 + y^2 = 1
since x = m, replace x with m to get:
m^2 + y^2 = 1
subtract m^2 from both sides of this equation to get y^2 = 1 - m^2
take the square root of both sides of this equation to get y = sqrt(1-m^2).
your triangles formed will have adjacent sides of m and opposite sides of sqrt(1 - m^2) and hypotenuse of 1.
you are given that cosine (12) = m
cosine = adjacent divided by hypotenuse, that means the adjacent side is equal to m.
you already calculated that opposite side is equal to sqrt(1-m^2).
since sine (12) = opposite divided by hypotenuse, that means that sine (12) is equal to sqrt(1 - m^2) / 1 which is equal to sqrt (1 - m^2).
you have 2 answers so far.
cosine (12) = m
sine (12) = sqrt(1 - m^2)
now to your last question.
you want to find tangent of 348 degrees.
the reference angle for 348 degrees is 360 - 348 which is equal to 12 degrees in the fourth quadrant.
12 degrees in the fourth quadrant is shown as -12 degrees.
-12 degrees is equivalent to 348 degrees.
you get -12 degrees by rotating clockwise from the 0 degree mark.
you get 348 degrees by rotating counter-clockwise from the 0 degree mark.
the angle is the same and the reference angle is 360 - 348 = 12 degrees as stated above.
a reference angle of 12 degrees in the fourth quadrant will have a hypotenuse of 1 and a cosine of m and a sine of -sqrt(1 - m^2).
the tangent of 348 degrees is equal to the tangent of -12 degrees which is equal to opposite side divided by adjacent side which is equal to -sqrt(1 - m^2) / m
