# Maths - Reciprocal Trig Functions

> Source: https://ollybritton.com/notes/a-level/maths/topics/reciprocal-trig-functions/ · Updated: 2021-02-20 · Tags: maths, further-maths, trigonometry

##### 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??
$$
\frac{\text{adj}}{\text{opp}}
$$

### 2021-02-22
##### $$\cos^2 x + \sin^2 x = 1$$ 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 $\csc^2 x$??
$$
1 + \cot^2 x = \csc^2 x
$$

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