If cosine theta = -2/5 and tangent theta > 0, what is the value of sine theta?

It is given that

cosθ = -2/5

We know that if tanθ > 0 cosθ < 0 then sinθ < 0 when θ is in third quadrant

We can use the formula

sinθ = -√(1 - cos2θ)

Substituting the values

sinθ = -√(1 - (-2/5)2)

sinθ = -√(1 - (4/25))

Taking LCM

sinθ = -√[25 - 4]/25

sinθ = -√(21/25)

sinθ = -√21/5

Therefore, the value of sinθ is -√21/5.