How is it possible to know all of the values of the unit circle by only knowing the values of sinx cosx and tanx of quadrant 1 angles and those on the axes?

Answer 1

Each angle may be used as a 'reference angle'. A 30 deg. angle in QI will have a sides, x = (sq rt 3)/2 , y= 1/2, r = 1. An angle of 150 deg (180 - 30) will create a triangle in Q2 with the same lengths except x is now negative. So if you know all trig values for 30, then change the signs for cos and tan because x is now negative and you know the values of all. Similarly for 210 deg (180+30) creates the same triangle in Q3 but both x and y values are neg. Sin and cos are neg, but tan (divide 2 neg's) is positive. In Q4 (360 - 30) creates a 330 deg angle for a triangle that is the same shape, but y is neg and x is pos so that sin and tan are neg but cos is pos.

ex: sin 30 = 1/2 (Q1), sin 150 = -1/2 (Q2), sin 210 = -1/2 (Q3), sin 330 = 1/2 (Q4)

notice only the sign (+/-) changes.

Most trig classes teach you that Q1 all trig functions are pos, Q2 sin is pos, Q3 tan is pos, Q4 cos is pos. Remember this and the 1st Quadrant values and then you can get all trig functions using the concept of a reference angle.