I guess that we know that the angle θ is in the fourth quadrant, and we know that:
cos(θ) = 9/19
now we want to find the value of sin(θ).
To do it, we can remember that for a point (x, y), such that we can define an angle β between the positive x-axis and a ray that connects the origin with the point (x, y), we can write the relations:
tan(β) = x/y
sin(β) = y/√(x^2 + y^2)
cos(β) = x/√(x^2 + y^2)
Because the angle is in the fourth quadrant, we know that:
x > 0
y < 0.
And we also know that:
cos(θ) = 9/19
then we have:
x = 9
√(x^2 + y^2) = √(9^2 + y^2) = √(81 + y^2) = 19
Solving the above equation we can find the value of y, that we need to remember, is negative:
√(81 + y^2) = 19
81 + y^2 = 19^2
y^2 = 19^2 - 81 = 280
y = √280 = -16.7
Now that we know the value of y, we can replace that in the sine equation to get:
sin(θ) = -16.7/19 = -0.879
If you want to learn more, you can read:
brainly.com/question/19830127
