Exact value of trig function

Question

given that sin(a) = -1/2 and tan(b) = 2/7 in the interval [pi/2, 3pi/2] what is the exact value of tan(A)?

Answer 1

sin210 = -1/2

sinA = -1/2 means A = 210 or 330, but only 210 is in the interval pi/2 to 3pi/2 which is 90 to 270 degrees

tanA = tan210 = exactly 1/sqr3 = (sqr3)/3

= about 0.577

not sure what tanb = 2/7 is about, other than if b is is in the same interval and it's positive, that means b is in quadrant III or I, eliminating quadrant IV or II, and eliminating A = 330 But you already knew the interval was from pi/2 to 3pi/3 which eliminates 330, leaving the only other possibility A=210

Answer 2

Find the angle a in (Pi/2, 3Pi/2) where Sin is equal to -1/2. Then find cos(a) and apply tan(a)=sin(a)/Cos(a).