If sin 𝜃 = − 3/5 and 𝜃 is in Quadrant III, find tan(𝜃/2).

Question

If  sin 𝜃 = −  3/5  and 𝜃 is in Quadrant III, find tan(𝜃/2).

Dayv O. · Accepted Answer

if 3p/2i<angle<pi (third quandrant) then 3pi/4,angle/2<pi/2 (2nd quadrant and tan of angle/2 is negative)

tan(angle/2)=+/- ((1-cos(angle))/(1+cos(angle))^(1/2) (the plus option for our problem)

this comes from half angle of sin divided by half angle cos

cos(angle)= -(1-sin²(angle)^(1/2) = -4/5,,,,, cos(angle) is negative in 3rd quadrant

tan(angle/2)=((1+4/5)/(1-4/5))^(1/2)=3

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