If © is an angle in standard position and its terminal side passes through the point (4,3), find the exact value of sin 0 in simplest radical form.

Answer 1

The slope of the line is a/b, which is the tangent of the angle, but we also know that a²+b²=1. We know that the line passes through the point (4,3), or y=mx is valid for 3=m*4 or m=3/4. Now a=3n, b=4n so that (3²+4²)n²=1, or n=1/√(3²+4²)=1/√(25)=1/5. The sine is always the numerator a, so a=3n=3/5. The sign of the square root is positive because it is in the first quadrant (++).

(The value of this sine corresponds to the Pythagorean triple 3²+4²=5²)

Answer 2

Draw and label a diagram!

sin θ = y-value / hypotenuse

y = 3

Use Pythagoras to determine hypotenuse.

Can yoiu calculate and anwer?