Question

why cos^2(x)+sin^2(x)=1?

Answer 1

Let Khan Academy explain it to you. Go there

Answer 2

please give the link

Answer 3

ABC is a right triangle

AC^2=AB^2+BC^2(pythagoras theorem)

divide each term by AC^2
\[\frac{AB^2}{AC^2}+\frac{BC^2}{AC^2}=\frac{AC^2}{AC^2}\]
\[(\frac{AB}{AC})^2+(\frac{BC}{AC})^2=1\]
\[[\frac{AB}{AC}=\frac{adjacent}{hypotenuse}=cosx,\frac{BC}{AC}=\frac{opposite}{hypotenuse}=sinx]\]
\[\therefore \cos^2x+\sin^2x=1\]

Answer 4

Thank You

Answer 5

Yeah but that still isn't a good explanation. How do you amazingly avoid explaining it in terms of the Unit Circle? I'm convinced this student has no clue what sine and cosine is in terms of the Unit Circle.