Answer:
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
