Sign In | Starter Of The Day | Tablesmaster | Fun Maths | Maths Map | Topics | More

International Baccalaureate Mathematics

Geometry and Trigonometry

Syllabus Content

Definition of the reciprocal trigonometric ratios secθ, cosecθ and cotθ.
Pythagorean identities:
1+tan2θ=sec2θ
1+cot2θ=cosec2θ
The inverse functions f(x)=arcsinx,
f(x)=arccosx,f(x)=arctanx; their domains and ranges; their graphs.

Here is an Advanced Starter on this statement:

Click on a topic below for suggested lesson Starters, resources and activities from Transum.


Furthermore

Formula Booklet:

Reciprocal trigonometric identities

\( \sec \theta = \frac{1}{\cos \theta} \)

\( \cosec \theta = \frac{1}{\sin \theta}\)

Pythagorean identities

\(1 + \tan^2 \theta = \sec^2 \theta \)

\( 1 + \cot^2 \theta = \cosec^2 \theta\)

Reciprocal trigonometric ratios are ratios that involve the reciprocal (or multiplicative inverse) of the trigonometric functions. The reciprocal ratios are the cosecant (cosec or csc), secant (sec), and cotangent (cot).

The formulas for the reciprocal ratios are as follows:

$$ \csc\theta = \frac{1}{\sin\theta} \\ \sec\theta = \frac{1}{\cos\theta} \\ \cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta} $$

Here is an example:

Given that \( \sin\theta = \frac{3}{5} \), find the values of \( \csc\theta \), \(\sec\theta \), and \(\cot\theta\).

$$ \csc\theta = \frac{1}{\sin\theta} = \frac{1}{\frac{3}{5}} = \frac{5}{3} $$ $$ \sec\theta = \frac{1}{\cos\theta} = \frac{1}{\sqrt{1 - \sin^2\theta}} = \frac{1}{\sqrt{1 - \left(\frac{3}{5}\right)^2}} = \frac{5}{4} $$ $$ \cot\theta = \frac{\cos\theta}{\sin\theta} = \frac{\sqrt{1 - \sin^2\theta}}{\sin\theta} $$ $$= \frac{\sqrt{1 - \left(\frac{3}{5}\right)^2}}{\frac{3}{5}} = \frac{4}{3} $$

Therefore, \( \csc\theta = \frac{5}{3}\), \(\sec\theta = \frac{5}{4}\), and \(\cot\theta = \frac{4}{3}\).

Screenshot below taken from Desmos Graphing Calculator (www.desmos.com) Cosec Graph Sec Graph Cot Graph

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.


Apple

©1997-2024 WWW.TRANSUM.ORG