Maths - Reciprocal Trig Functions

Definitions as reciprocals

What is $\csc\theta$?

\[\frac{1}{\sin\theta}\]

What is $\sec\theta$?

\[\frac{1}{\cos\theta}\]

What is $\cot\theta$?

\[\frac{1}{\tan\theta}\]

What is $\csc\theta$ in terms of triangle sides?

\[\frac{\text{hyp}}{\text{opp}}\]

What is $\sec\theta$ in terms of triangle sides?

\[\frac{\text{hyp}}{\text{adj}}\]

What is $\cot\theta$ in terms of triangle sides?

\[\frac{\text{adj}}{\text{opp}}\]

\[\cos^2 x + \sin^2 x = 1\]

What do you get if you divide both sides by $\cos^2 x$?

\[1 + \tan^2 x = \sec^2 x\]

\[\sin^2 x + \cos^2 x = 1\]

What do you get if you divide both sides by $\sin^2 x$?

\[1 + \cot^2 x = \csc^2 x\]

What is the identity linking $\tan^2 x$ and $\sec^2 x$?

\[1 + \tan^2 x = \sec^2 x\]

What is the identity linking $\cot^2 x$ and $\csc^2 x$?

\[1 + \cot^2 x = \csc^2 x\]