Question

evaluate the function for the given values..... f(x)=sin^2(x)+cos^2(x) where x=9 pie/4

Answer 1

\[\sin ^{2} x + \cos ^{2} x where x=9\pi/4\]

Answer 2

sin^2(x) + cos^2(x) = 1, so it doesn't matter what x is, the answer will always be 1.

Answer 3

why?

Answer 4

If you have a circle of radius 1, and you want the cos or sin of any angle, you can just trace a radius at that angle, the vertical line projected from the radius line gives the sin, the horizontal, the cos.
You'll see that it forms a right triangle of hyp. 1. hyp^2 = a^2 + b^2. In this case a and b are sin and cos.

Answer 5

Draw a right triangle whose hypotenuse is 1. Then label the base x and the height y. Use the definition that the sin(theta) = opposite/hypotenuse = y/1 = y. So the height is sin(theta). Likewise, cos(theta) = adjacent/hypotenuse = x/1 = x. So the base length is cox(theta).
Now apply the Pythagorean Theorem to get cos^2(theta) + sin^2(theta) = 1^2
cos^2(theta) + sin^2(theta) = 1. And you have the Pythagorean Identity.