The terminal side of an angle in standard position passes through p(15, –8). what is the value of sin theta?

Check the picture below.

Sin theta = -8/17 ≈ - 0.471

Step-by-step explanation:

Right triangles on a Cartesian plane using a point are created by drawing a line from the point to the x-axis and a line to the origin (0, 0).

The angle of reference, in this case theta, is created at the origin.

Remember the trigonometry ratios can be remembered using SOHCAHTOA.

SOH is Sin ∡ = Opposite / Hypotenuse. The "A" means adjacent.

On a Cartesian plane, opposite, adjacent and hypotenuse change.

opposite = y

adjacent = x

hypotenuse = r

Sin ∡ = y/r

For the point P(15, -8), x =15 and y = -8.

To find r, use the equation of a circle: x² + y² = r²

Substitute x=15 and y= -8

x² + y² = r²

15² + (-8)² = r²

r² = 289

r = √289

r = 17

Substitute r=17 and y= -8 into the equation for Sine.

Sin ∡ = y/r

Sin theta = -8/17  Exact value

Sin theta ≈ -0.471   Rounded to three decimal places

yes. we do proportions in probabilities.

ratio is 2 : 9

the answer is three

13.5 : 3