Trigonometry

Question 1

Finding angles on a straight line

Answer 1

Angles on a straight line sum to 180°

⦣’s on line

Question 2

Finding angles at a point

Answer 2

Angles at a point sum to 360°

⦣’s at a pt

Question 3

Finding angles on intersecting lines

Answer 3

Vertically opposite angles are equal

Vert. opp. ⦣’s =

Question 4

Finding interior angles of a triangle

Answer 4

Interior angles of a triangle sum to 180°

⦣ sum of △

Question 5

Finding angles of a triangle (2)

Answer 5

1. Angles in an equilateral triangle are 60°

Equilat. △

2. Base angles in an isosceles triangle are equal

Isos. △, base ⦣’s =

Question 6

Finding angles of a trapezium

Answer 6

Base angles in an isosceles trapezium are equal

Isos. trapezium, base ⦣’s =

Question 7

Finding exterior angles of a triangle

Answer 7

Exterior angle of a triangle is equal to the sum of the interior opposite angles

Ext ⦣ of △ = sum of int. opp. ⦣’s

Question 8

Finding angles on parallel lines (3)

Answer 8

1. Alternate angles on parallel lines are equal

Alt. ⦣’s = , || lines

2. Corresponding angles on parallel lines are equal

Corresp. ⦣’s = , || lines

3. Co-interior angles on parallel lines sum to 180°

Co-int. ⦣’s, || lines

Question 9

Finding angles of a parallelogram

Answer 9

Opposite interior angles in a parallelogram are equal

Opp. int ⦣’s, parallelogram, =

Question 10

Finding angles of a polygon (3)

Answer 10

1. Interior angles of an n-sided polygon are equal to (n-2) x 180°

Int. ⦣ sum polygon, (n-2) x 180°

2. Exterior angles of a polygon sum to 360°

Ext. ⦣’s of polygon

3. Exterior angle of an n-sided regular polygon is equal to 360° / n

Ext. ⦣, reg. polygon

Question 11

Finding angles of a triangle in a circle (2)

Answer 11

1. Isosceles triangle from equal radii in a circle, with base angles equal, has an angle sum of 180°

= radii, isos. △, ⦣ sum

2. Isosceles triangle from equal radii in a circle has base angles equal

= radii, isos. △, base ⦣’s =

Question 12

Finding angles at the centre and circumference of a circle

Answer 12

Angle at the centre of a circle is equal to 2 x the angle at the circumference

⦣ at centre = 2 x ⦣ at circumf.

Question 13

Finding angles on the diameter of a circle

Answer 13

Angle standing on the diameter is equal to 90°

⦣ in semi-circle

Question 14

Finding angles of the arc of a circle

Answer 14

Angles standing on the same arc are equal

⦣’s on same arc

Question 15

Finding angles of a cyclic quadrilateral (2)

Answer 15

• Cyclic quadrilaterals have all 4 vertices touching the circumference of the circle

1. Opposite angles in a cyclic quadrilateral add to 180°

Cyc. quad., opp. ⦣’s

2. Exterior angle of a cyclic quadrilateral is equal to the interior opposite angle

Cyc. quad., ext. ⦣ = int. opp. ⦣

Question 16

Finding angles of tangents in a circle (2)

Answer 16

1. Tangent of a circle is perpendicular to the radius at the point of contact

Tgt. ⟂ rad.

2. Tangents from a point to a circle are equal

= Tgts.

Question 17

Finding angles of segments in a circle

Answer 17

Angle between a chord and a tangent is equal to the angle in the opposite segment

⦣ between tgt. & chord = ⦣ on chord in opp. segment

Question 18

The formula for the circumference of a circle

Answer 18

2 x r x π
OR
d x π

Question 19

The formula for the area of a circle

Answer 19

π x r^2

Question 20

The formula for the angle of any triangle

Sine rule

Answer 20

Sin (A) Sin (B) Sin (C)
_____ = _____ = _____
a b c

Question 21

a b c
_____ = _____ = _____
Sin (A) Sin (B) Sin (C)

Answer 21

The formula for the side of any triangle

Sine rule

Question 22

cos (A) = b^2 + c^2 - a^2
_____________
2bc

Answer 22

The formula for the angle of any triangle

Cosine rule

Question 23

a^2 = b^2 + c^2 - 2bc cos (A)

Answer 23

The formula for the side of any triangle

Cosine rule

Question 24

Sector

Answer 24

The area between the center point and 2 radius of a circle

Question 25

Segment

Answer 25

The area between the circumference and chord of a circle

Question 26

Ambiguous case

Answer 26

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.

Question 27

How to convert from degrees to radians

Answer 27

x by π / 180

Question 28

How to convert from radians to degrees

Answer 28

x by 180 / π

Question 29

Where are angles of depressions and elevation taken?

Answer 29

Elevation - From the horizontal, upwards | Depression - From the horizontal, downwards

Question 30

Rules to follow when simplifying equations

Answer 30

- 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.