Geometry problem
Sections:
1) Revision notes
2) Practice questions
Revision notes
Sine rule, cosine rule and special angles in trigonometry
TOA, CAH, SOH for right-angled triangle
$ \tan \theta = $ $ \phantom{.} {Opp \over Adj} $, $ \cos \theta = $ $ \phantom{.} {Adj \over Hyp} $, $ \sin \theta = $ $ \phantom{.} {Opp \over Hyp} $
Pythagoras theorem
$ a^2 + b^2 = c^2 $
Trigonometric ratio of special angles
| $30^\circ \text{ or } {\pi \over 6}$ | $45^\circ \text{ or } {\pi \over 4}$ | $60^\circ \text{ or } {\pi \over 3}$ | |
|---|---|---|---|
| $\sin \theta$ | $ \phantom{.} {1 \over 2} $ | $ \phantom{.} {1 \over \sqrt{2}} $ | $ \phantom{.} {\sqrt{3} \over 2} $ |
| $\cos \theta$ | $ \phantom{.} {\sqrt{3} \over 2} $ | $ \phantom{.} {1 \over \sqrt{2}} $ | $ \phantom{.} {1 \over 2} $ |
| $\tan \theta$ | $ \phantom{.} {1 \over \sqrt{3}} $ | $ \phantom{.} 1 $ | $ \phantom{.} \sqrt{3} $ |
Geometry formulas (provided)
\begin{align*} \text{Sine rule: } & {a \over \sin A} = {b \over \sin B} \\ \\ \text{Cosine rule: } & a^2 = b^2 + c^2 - 2bc \cos A \\ \\ \text{Area of triangle} & = {1 \over 2} a b \sin C \end{align*}
Practice questions
Use sine rule and Pythagoras theorem in geometry proofs
1. The diagram shows a triangle $ABC$ in which $AC = x$ cm, $\angle BAD = y^\circ$ and $\angle BCA = 90^\circ$. The midpoint of $BC$ is $D$ and $\angle BAC = 30^\circ$.
(from Mentor book)
(i) Show that the length of $AD$ is $ {\sqrt{a} \over b} x$ cm, where $a$ and $b$ are integers to be determined.
(ii) Show that $y^\circ = \sin^{-1} \left(\sqrt{39} \over 26\right)$.
O Level past year questions on trigonometry in geometry problems
| Year & paper | Comments |
|---|---|
| 2012 P1 Question 2 | Link - Subscription required |
| 2008 P1 Question 1 | Link - Subscription required |
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