Trigonometric expressionsFurther examples on the addition formula
The addition formulae and trigonometric identities are used to simplify or evaluate trigonometric expressions. Trigonometric equations are solved using a double angle formulae and the wave function.
Here's another example to work through. This time you need to draw two right-angled triangles to help you with your working.
Question
If \(\sin p = \frac{3}{5}\) and \(\tan q = \frac{5}{{12}}\) where \(0 \le p \le \frac{\pi }{2}\) and \(0 \le q \le \frac{\pi }{2}\), find the exact value of \(\sin (p - q)\).
From \(\sin p = \frac{3}{5}\)
From \(\tan q = \frac{5}{{12}}\)
Use Pythagoras' theorem to work out the third side of each of these triangles. Then insert these values into your working as follows.