We think you are located in South Africa. Is this correct?

# Practise now to improve your marks

You can do it! Let us help you to study smarter to achieve your goals. Siyavula Practice guides you at your own pace when you do questions online.

## 6.6 Summary (EMBHT)

 square identity quotient identity $$\cos^2\theta + \sin^2\theta = 1$$ $$\tan\theta = \dfrac{\sin\theta}{\cos\theta}$$ negative angles periodicity identities co-function identities $$\sin (-\theta) = - \sin \theta$$ $$\sin (\theta \pm \text{360}\text{°}) = \sin \theta$$ $$\sin (\text{90}\text{°} - \theta) = \cos \theta$$ $$\cos (-\theta) = \cos \theta$$ $$\cos (\theta \pm \text{360}\text{°}) = \cos \theta$$ $$\cos (\text{90}\text{°} - \theta) = \sin \theta$$
 sine rule area rule cosine rule $$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$$ area $$\triangle ABC = \frac{1}{2} bc \sin A$$ $$a^2 = b^2 + c^2 - 2 bc \cos A$$ $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ area $$\triangle ABC = \frac{1}{2} ac \sin B$$ $$b^2 = a^2 + c^2 - 2 ac \cos B$$ area $$\triangle ABC = \frac{1}{2} ab \sin C$$ $$c^2 = a^2 + b^2 - 2 ab \cos C$$ General solution:

1. \begin{align*} \text{If } \sin \theta &= x \\ \theta &= \sin^{-1}x + k \cdot \text{360}\text{°} \\ \text{or } \theta &= \left( \text{180}\text{°} - \sin^{-1}x \right) + k \cdot \text{360}\text{°} \end{align*}
2. \begin{align*} \text{If } \cos \theta &= x \\ \theta &= \cos^{-1}x + k \cdot \text{360}\text{°} \\ \text{or } \theta &= \left( \text{360}\text{°} - \cos^{-1}x \right) + k \cdot \text{360}\text{°} \end{align*}
3. \begin{align*} \text{If } \tan \theta &= x \\ \theta &= \tan^{-1}x + k \cdot \text{180}\text{°} \end{align*}

for $$k \in \mathbb{Z}$$.

How to determine which rule to use:

• Area rule:

• no perpendicular height is given
• Sine rule:

• no right angle is given
• two sides and an angle are given (not the included angle)
• two angles and a side are given
• Cosine rule:

• no right angle is given
• two sides and the included angle angle are given
• three sides are given