Answer :
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
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