If sin θ = 2 over 3 and tan θ < 0, what is the value of cos θ?

square root 5 over 2
negative square root of 5
square root of 5 over 3
negative square root of 5 over 3

Sinθ = (2/3)    tanθ < 0  Implies tanθ = Negative.

For sin positive and tan negative, implies θ is in the second quadrant.

Sinθ = (2/3) = opposite / Hypotenuse.

Adjacent side:

x² + 2² = 3²

x² + 4 = 9

x² = 9 - 4

x² = 5

x = √5 = Adjacent.

cosθ  =  Adjacent / Hypotenuse =  √5 / 3

Since θ is in the second quadrant, cosine is also negative in the second quadrant.


Therefore:

cosθ  =  - (√5/3)

The last option from the top :  negative square root of 5 over 3

21 is the answer the answer is 21