20 points do you see a pattern? do you think this will always be true? why or why not?

Hello from MrBillDoesMath!

  (sin(@)) ^2 +  (cos(@)) ^2 = 1  for all angles @.

Discussion ;

Take a point,  say in the first quadrant. on a unit circle (circle with radius 1) Let that point by (x,y). The from the Pythagorean theorem.

x^2 + y^2 = r^2   or as r = 1

x^2 + y ^2 = 1             ("Equation 1")

If you drop a line from (x,y) perpendicular to the x axis you find that

y = r [email protected] or y = [email protected] as r =1.

and

x = r [email protected] or x = [email protected] as r = 1

(Look at the triangle formed by the radius, the perpendicular line and the positive x axis).  Substitute these x and y values in  Equation 1 above. This gives

([email protected])^2 +  ([email protected])^2 =1

which is true for all angles. This is a key "pattern" or identity that you should commit to long term memory!

Regards, MrB

chiken

step-by-step explanation: