Trigonometry

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Bearings

A bearing measures the movement of an angle in a clockwise direction and always on the north line. The bearing of a point is the line joining the centre of the compass through the point measured in degrees in a clockwise way from the north direction.

Congruency & Transformations

The common relation between geometric figures is congruency. The shapes or figures are congruent if the length of the sides and angles measure the same.

Pythagoras Theorem

Pythagoras Theorem Consider the triangle \(ΔPMK, P = 90^{∘}\) A triangle is called a right-angled triangle if one of its angles is \(90^{∘}\). So, ΔPMK is a right-angled triangle (or rectangular triangle) with right-angle \(\angle P\). 

Sine and Cosine Rule

There are different kinds of triangle: a right, acute and obtuse triangle. Solving for the sides of a right triangle, we commonly used the Pythagorean theorem. 

Triangle Intercept Theorem

If CB and DE are parallel, the ratio of CD to DA and the ratio of BE to EA are equal. In other words, CD/DA = BE/EA . This is often a useful way of solving triangle problems and can be derived from the properties of similar triangles.

Sine and Cosine Formulae

sin x = sin (180 – x) e.g. sin 130 = sin (180 – 130) = sin 50 cos x = -cos (180 – x) The Sine Rule: This works in any triangle:  a    =    b    =    c   sinA     sinB      sinC alternatively, sinA = sinB = sinC a

Sin, Cos, Tan Graphs

The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle.

Similar Triangles

If two shapes are similar, one is an enlargement of the other. This means that the two shapes will have the same angles and their sides will be in the same proportion (e.g. the sides of one triangle will all be 3 times the sides of the other etc.).