Question

Find the exact value of sin (arccos (3/5)). For full credit, explain your reasoning.

Answer 1

The equation for cosine is cos(x)=Adjacent/Hypotenuse
The inside trig function is arccos(3/5), which means cos(x)=3/5. Comparing cos(x)=Adjacent/Hypotenuse with cos(x)=3/5

Find Adjacent=3 and Hypotenuse=5.
Then, using the Pythagorean theorem, find Opposite=?
a² = c² - b²
a² = 5² - 3² = 25 - 9 = 16
a = √16 = 4

Adjacent=3Opposite=4Hypotenuse=5

Plug in the value for sin(x) = opposite/hypotenuse

sin(x) = 4/5