We are familiar with the Pythagorean theorem (a²+b²=c²) and the Pythagorean identity in trigonometry (cos²(θ)+sin²(θ)=1), but how do these two concepts that share a name relate?
This applet is designed to help us explore the Pythagorean identity visually and mathematically as the Pythagorean theorem. Click "Start Movie!" for a step-by-step walkthrough.
Now let's explore this a little more on our own.
How could we manipulate the Pythagorean identity using these basic trigonometric identities?
csc(θ)=
1
/
sin(θ)
sec(θ)=
1
/
cos(θ)
cot(θ)=
cos(θ)
/
sin(θ)
=
1
/
tan(θ)