Trigonometry Flashcards
Finding angles on a straight line
Angles on a straight line sum to 180°
⦣’s on line
Finding angles at a point
Angles at a point sum to 360°
⦣’s at a pt
Finding angles on intersecting lines
Vertically opposite angles are equal
Vert. opp. ⦣’s =
Finding interior angles of a triangle
Interior angles of a triangle sum to 180°
⦣ sum of △
Finding angles of a triangle (2)
- Angles in an equilateral triangle are 60°
Equilat. △
- Base angles in an isosceles triangle are equal
Isos. △, base ⦣’s =
Finding angles of a trapezium
Base angles in an isosceles trapezium are equal
Isos. trapezium, base ⦣’s =
Finding exterior angles of a triangle
Exterior angle of a triangle is equal to the sum of the interior opposite angles
Ext ⦣ of △ = sum of int. opp. ⦣’s
Finding angles on parallel lines (3)
- Alternate angles on parallel lines are equal
Alt. ⦣’s = , || lines
- Corresponding angles on parallel lines are equal
Corresp. ⦣’s = , || lines
- Co-interior angles on parallel lines sum to 180°
Co-int. ⦣’s, || lines
Finding angles of a parallelogram
Opposite interior angles in a parallelogram are equal
Opp. int ⦣’s, parallelogram, =
Finding angles of a polygon (3)
- Interior angles of an n-sided polygon are equal to (n-2) x 180°
Int. ⦣ sum polygon, (n-2) x 180°
- Exterior angles of a polygon sum to 360°
Ext. ⦣’s of polygon
- Exterior angle of an n-sided regular polygon is equal to 360° / n
Ext. ⦣, reg. polygon
Finding angles of a triangle in a circle (2)
- Isosceles triangle from equal radii in a circle, with base angles equal, has an angle sum of 180°
= radii, isos. △, ⦣ sum
- Isosceles triangle from equal radii in a circle has base angles equal
= radii, isos. △, base ⦣’s =
Finding angles at the centre and circumference of a circle
Angle at the centre of a circle is equal to 2 x the angle at the circumference
⦣ at centre = 2 x ⦣ at circumf.
Finding angles on the diameter of a circle
Angle standing on the diameter is equal to 90°
⦣ in semi-circle
Finding angles of the arc of a circle
Angles standing on the same arc are equal
⦣’s on same arc
Finding angles of a cyclic quadrilateral (2)
• Cyclic quadrilaterals have all 4 vertices touching the circumference of the circle
- Opposite angles in a cyclic quadrilateral add to 180°
Cyc. quad., opp. ⦣’s
- Exterior angle of a cyclic quadrilateral is equal to the interior opposite angle
Cyc. quad., ext. ⦣ = int. opp. ⦣
Finding angles of tangents in a circle (2)
- Tangent of a circle is perpendicular to the radius at the point of contact
Tgt. ⟂ rad.
- Tangents from a point to a circle are equal
= Tgts.
Finding angles of segments in a circle
Angle between a chord and a tangent is equal to the angle in the opposite segment
⦣ between tgt. & chord = ⦣ on chord in opp. segment
The formula for the circumference of a circle
2 x r x π
OR
d x π
The formula for the area of a circle
π x r^2
The formula for the angle of any triangle
Sine rule
Sin (A) Sin (B) Sin (C)
_____ = _____ = _____
a b c
a b c
_____ = _____ = _____
Sin (A) Sin (B) Sin (C)
The formula for the side of any triangle
Sine rule
cos (A) = b^2 + c^2 - a^2
_____________
2bc
The formula for the angle of any triangle
Cosine rule
a^2 = b^2 + c^2 - 2bc cos (A)
The formula for the side of any triangle
Cosine rule
Sector
The area between the center point and 2 radius of a circle
Segment
The area between the circumference and chord of a circle
Ambiguous case
When the shorter of the 2 given sides is opposite the given angle. (This means that 2 different triangles with the same measurements can be drawn (acute and obtuse).
- Be careful to solve for the correct triangle based on the context of the question.
How to convert from degrees to radians
x by π / 180
How to convert from radians to degrees
x by 180 / π
Where are angles of depressions and elevation taken?
Elevation - From the horizontal, upwards
Depression - From the horizontal, downwards
Rules to follow when simplifying equations
- When simplifying the numbers at the end, only add/subtract or multiply/divide according to their sign
(like terms only can be combined)
If there are brackets, first multiply the terms outside the brackets together, then expand the brackets by multiplying the new term outside the brackets with the terms inside. - Expand brackets and write in their full form
- Write out numbers which are squared in their full form
- Square roots and square powers cancel out
- Write out sin/cos numbers out in their full form
- When simplifying to get only the formula for the a angle term at the end (if using the sin rule), you can combine the sin( ) side 2 value and the x side 1 value by multiplying, and leaving the result on the top half of the fraction.
