8.1 Q-11 | Fundamentals Of Trigonometry | Mathematics 11

Exercise 8.1 — Question 11

This question applies the fundamental law of trigonometry and the sine/cosine addition and subtraction formulas.

$sin (α + β) = sin α cos β + cos α sin β$

$sin (α - β) = sin α cos β - cos α sin β$

$cos (α + β) = cos α cos β - sin α sin β$

$cos (α - β) = cos α cos β + sin α sin β$

Note: For $cos (α \pm β)$ , the sign between the terms is opposite to the operator between the angles.

When simplifying expressions of the form:

Simplify: $sin 13 8^{\circ} cos 4 6^{\circ} - cos 13 8^{\circ} sin 4 6^{\circ}$

Solution:

Recognise the pattern $sin A cos B - cos A sin B = sin (A - B)$ :

$sin 13 8^{\circ} cos 4 6^{\circ} - cos 13 8^{\circ} sin 4 6^{\circ} = sin (13 8^{\circ} - 4 6^{\circ}) = sin 9 2^{\circ}$