Question

If tan A = 1/2 then the value of 'SinA' if angle A lies in the 3rd quadrant is

Answer 1

Answer:

given that:

tanA=1/2

find:sinA=?

solution:

1+tan²A=sec²A

sec²A=1+(1/2)²

sec²A=1+1/4

sec²A=5/4

secA=√5/2

cosA=1/secA

cosA=1/√5/2

cosA=2/√5

sin²A+cos²A=1

sin²A=1-cos²A

sin²A=1-(2/√5) ²

sin²A=1-4/5

sin²A=1/5

sinA=1/√5

sinA is negative in third quadrant, then

sinA = -1/√5