Maths

• A Tangent and a radius meet at 90 degrees
• A Tangent is a line that just touches a single point on the circumference of a circle
• A Tangent always makes an angle of exactly 90 degrees with the radius it meets at this point
• Two Radii form an Isosceles Triangle
• The Perpendicular Bisector of a Chord passes through the Centre of the circle
• A Chord is any line draw across a circle
• when a chord is cut exactly in half at 90 degrees, will go through the centre of the circle
• The angle at the centre of a circle is twice the angle at the circumference
• The Angle in a semicircle is 90 degrees
• Angles in the same segment are equal
• The two angles on opposite sides of the chord add up to 180 degrees
• Opposite angles in a cyclic quadrilateral add up to 180 degrees
• A cyclical quadrilateral is a 4-sided shape with every corner touching the circle
• Tangents from the same point are the same length
• two tangents drawn from an outside point are always equal in length, creating two congruent right-angled triangles
• The Alternate Segment Theorem
• The angle between a tangent and a chord is always equal to 'the angle in the opposite segment'
• what is the sine rule

  $\frac{a}{\sin\ A\ }=$$\frac{b}{\sin\ B}=$$\frac{c}{\sin\ C}$
• what is the normal form of the cosine rule

  $a^2=$$b^2+$$c^2-2bc\ \cos\ A$
• what is the rearranged form of the cosine rule to find the angle

  $\cos\ A\ =$$\ \frac{b^2\ +\ c^2-a^2}{2bc}$
• Area of a triangle = $\frac{1}{2}ab\ \sin\ C$
• $\sin30^{\circ}$


  $\frac{1}{2}$
• $\sin60^{\circ}$


  $\frac{\sqrt{3}}{2}$
• $\sin45^{\circ}$


  $\frac{1}{\sqrt{2}}$
• $\sin0^{\circ}$


  0
• $\sin90^{\circ}$


  $1$
• $\cos30^{\circ}$


  $\frac{\sqrt{3}}{2}$
• $\cos60^{\circ}$


  $\frac{1}{2}$
• $\cos45^{\circ}$


  $\frac{1}{\sqrt{2}}$
• $\cos0^{\circ}$


  $1$
• $\cos90^{\circ}$


  $0$
• $\tan30^{\circ}$


  $\frac{1}{\sqrt{3}}$
• $\tan60^{\circ}$


  $\sqrt{3}$
• $\tan45^{\circ}$


  $1$
• $\tan0^{\circ}$


  $0$