**19.2- Pythagoras’ theorem**

Know the formulae for: Pythagoras’ theorem a^{2}+ b^{2}=c^{2} , and the

trigonometric ratios,

\({sin θ}\) = \(\frac{opposite}{hypotenuse}\)

\({cos θ}\) = \(\frac{adjacent}{hypotenuse}\)

\({tan θ}\) = \(\frac{ opposite}{adjacent}\)

Apply them to find angles and lengths in right-angled triangles in two-dimensional figures

**19.3-Trigonometry 1**

• Interpret and use three-figure bearings

• apply Pythagoras’ theorem and the sine, cosine and tangent ratios for

acute angles to the calculation of a side or of an angle of a right-angled

triangle

• solve trigonometrical problems in two dimensions involving angles of

elevation and depression

• extend sine and cosine functions to angles between 90° and 180°

• solve problems using the sine and cosine rules for any triangle and the

formula area of triangle = \(\frac{1}{2}abc sin c\)

• solve simple trigonometrical problems in three dimensions

**19.4-Trigonometry 2**

Measured clockwise from the north, i.e. 000°–360°.

e.g. Find the bearing of A from B if the bearing of B from A is 125°

Angles will be quoted in, and answers required in, degrees and decimals of a degree to one decimal place.

Calculations of the angle between two planes or of the angle between

a straight line and plane will not be required.

**19.5-Pythagoras and Trigonometry problem**

Know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°;

know the exact value of tan θ for θ = 0°, 30°, 45° , 60° and 90°

**19.6- Vectors**

• Describe a translation by using a vector represented by

\(\dbinom{x}{y}\), \(\vec{AB}\) or **a**

• add and subtract vectors

• multiply a vector by a scalar

• calculate the magnitude of a vector\(\dbinom{x}{y}\) as \(\sqrt{x^2 + y^2}{y}\)

• represent vectors by directed line segments

• use the sum and difference of two vectors to express given vectors in

terms of two coplanar vectors

• use position vectors

**19.7 – Summary and Review**

**Question1 :** If \(\vec{a}\) = \(\dbinom{6}{-10}\) , \(\vec{b}\) = \(\dbinom{-1}{2}\) and \(\vec{c}\) = \(\dbinom{-4}{7}\)

Calculate \(\vec{a} + \vec{b} + \vec{c}\) and Show that \(\vec{a} + 2\vec{c}\) = \(k\vec{b}\) where k is an integer ?

**19.8- Assessment 19**

**Question 1** : Use trigonometry to work out the length x ?

**Question 2 :** The vector \(\dbinom{3}{2}\) translates A to B. Calculate the vector that translates B to A ?

**Question 3 :** Given the triangle ABC such that AB=15 cm, \(\cap{A}\) =34°, \(\cap{B}\) =42°, \(\cap{C}\) =104°, Calculate AC ?

**Question 4 :** Solve the following equations :

cosx= cos 60° ( for 90°≤x≤306°)

cosx=- cos 60° ( for 180°≤x≤360°)

**Question 5 :** Lisa and Tila are walking towards a shop along different straight paths.

The diagram shows their positions at 2 pm

Assume they walk at the same speed. Who will arrive at the shop first?