Find the trigonometric function value of angle θ. Cos θ = 2/7 and θ is in quadrant IV. Find sin θ.

cosØ = x/r = 2/7

so x=2 , r = 7
2^2 + y^2 = 7^2
y^2 = 45 = ± 3√5
but we are in IV , so y = -3√5

sinØ = -3√5/7

To find the value of sin θ when cos θ = 2/7 and θ is in quadrant IV, we can use the Pythagorean identity:

sin^2 θ + cos^2 θ = 1.

Since θ is in quadrant IV, which means it is negative, cos θ is positive and sin θ is negative. Therefore, we will use the negative square root in the equation above.

First, solve for sin^2 θ:

sin^2 θ = 1 - cos^2 θ
= 1 - (2/7)^2
= 1 - 4/49
= 45/49.

Now, take the square root of both sides:

sin θ = -√(45/49)
= -(√45/√49)
= -(√45/7).

Hence, sin θ is equal to -(√45/7).