You can put this solution on YOUR website! you are working with the unit circle.
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
