jeef said:
given point is on the terminal side of an angle in standard position. Determine the exact value of the cosine of x. ( -4, 10 )
If A is an angle in standard position (initial side on the positive x-axis), and (x, y) is a point on the terminal side of A, then
sin A = y / r; cos A = x / r; and tan A = y / x
r = sqrt(x<SUP>2</SUP> + y<SUP>2</SUP>)
In your case, x = -4, y = 10, and r = sqrt((-4)<SUP>2</SUP> + 10<SUP>2</SUP>)
r = sqrt(116)
cos A = -4 / sqrt(116)
You can simplify sqrt(116), since 116 is 4*29. sqrt(116) = 2 sqrt(29)
cos A = -4 / [2 sqrt(29)] or, reducing the fraction
cos A = -2 / sqrt(29)
It's not considered "good form" to leave a radical in the denominator of a fraction. Multiply numerator and denominator by sqrt(29):
cos A = [-2 sqrt(29)] / 29
Now....the directions for the problem said to find the "exact value" so STOP HERE. Do not reach for your calculator.
