Question

If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ?

negative square root 21

negative square root 21 over 5

square root 21 over 5

square root of 21 over 2

Answer 1

If cos(teta) is negative number that means that angle teta is in either second or third quadrant of x-y coordinate system. Now, because tan( teta) is greater than 0 that means that teta is in either first or third quadrant.

Knowing both of these conditions we can conclude that teta is in third quadrant.
Sin of angle in third quadrant is negative. Now we need to calculate its value.
sin^2(teta) = 1-cos^2(teta)
sin^2(teta) = 1-4/25 = 21/25

sin(teta) = -√21/5

answer is second option