Let alpha be an angle in the third quadrant such that tan alpha = \(4/7\). Compute cos alpha.
Since tan = y / x and both the x value and the y value are negative in the third quadrant,
y = -4 and x = -7.
Since r = sqrt( x2 + y2 ) ---> r = sqrt( (-7)2 + (-4)2 ) ---> r = sqrt( 65 )
Since cos = x / r ---> cos = -7 / sqrt( 65 )