Since $\cos \theta$ and $sin \theta$ are the $x$ and $y$ coordinate of a point on the unit circle, we can write the first pythagorean Identity based on a right triangle that has the radius for the hypotenuse: $\cos^2 \theta+ \sin^2 \theta=1$ The next follows from scaling the original triangle up by dividing the sides by $\cos\theta$ $1 + \tan^2 \theta=\sec^2\theta$ The next follows from scaling the original triangle up by dividing the sides by $\sin\theta$ $\cot^2 \theta+ 1=\csc^2 \theta$ Below, diagrams are attached which show the similar triangles. (Notice that $\tan\theta$ is the length of a vertical tangent segment and $\cot\theta$ is the length of a horizontal tangent segment ![[pyth-id-diag-1.svg]] ![[pyth-id-diag-2.svg]]