Let Pxy denote the point where the terminal side of an angle

Let P(x,y) denote the point where the terminal side of an angle meets the unit circle. Use the given information to evaluate the six trigonometric functions of .

46. P is in Quadrant II and y= 2/7

Solution

Let the origin be O, and the point on the x-axis at x = -(45/49) be Q then form the OQP where QOP = which is supplementary to , that is = 180 - . Let OP be represented by r.
y = QP can be readily calculated as 2/7

In the 2nd quadrant, the value of x is negative and the values of y and r are positive.
Thus the sine ratio y/r is positive, the cosine ratio x/r is negative, and the tangent ratio y/x is negative.

Then sin = +sin = (2/7) /1 = 2/7 : cosecant = 7/2
cos = -cos = (-(45/49)) / 1 = -(45/49) : secant = 1/(-(45/49)) = --(49/45)
tan = -tan = (2/7) / (-(45/49) = -2/45 : cotangent = -(45)/2