Question

Which description is the basis of proof that sin^2 x + cos^2 x= 1 ?

A. trigonometric identity, which states that tan x = (sin x / cos x)

B. equation of a circle with (0,0) as its center and radius = 1

C. law of sines and law of cosines

D. definition of the tangent ratio

Answer 1

Answer: Choice B
Equation of a circle with (0,0) as its center and radius = 1

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Step-by-step explanation:

Recall that the unit circle is the equation
x^2 + y^2 = 1
This is a circle with center (h,k) = (0,0) and radius r = 1
It is in the form
(x-h)^2 + (y-k)^2 = r^2

We can write the first equation mentioned in the form sin^2(t)+cos^2(t) = 1
Using
x = cos(t)
y = sin(t)
t = angle

The point P(x,y) on the unit circle has an x coordinate of cos(t) and a y coordinate of sin(t). We can see this through drawing a right triangle.