Question

angle 0 is in quadrant I with cos 0 is 10/17. which of the following would be the appropriate step in calculating the value of sin 0 using the pythagorean identity?

a. sin 0 + (10/17)^2 = 1
b. sin 0 - (10/17)^2 = 1
c. sin^2 0 + (10/17)^2 = 1
d. sin^2 0 - (10/17)^2 = 1

Answer 1

Answer: Choice C

Work Shown:

$\sin^2(\theta) + \cos^2(\theta) = 1\\\\\sin^2(\theta) + \left(\cos(\theta)\right)^2 = 1\\\\\sin^2(\theta) + \left(\frac{10}{17}\right)^2 = 1$

As the name implies, the pythagorean identity uses the pythagorean theorem for right triangles. The 1 on the right hand side is the length of the hypotenuse, which is the radius of the unit circle.