Trigonometry

Worked examples (13)extended set

• 1Finding a side
• 2Finding an angle
• 3Combining Pythagoras with trigonometry
• 4Angle of elevation in context
• 5Angle of depression
• 6One unknown in two triangles
• 7Exact values in a composite figure
• 8Elevation and depression from one window
• 9Working backwards from a regular octagon
• 10Exact values and a side in surd form
• 11A roof frame: a surd length and a vertical post
• 12Shortest distance from a point to a line
• 13Two right-angled triangles in terms of k

Worked examples (12)extended set

• 1Back bearings
• 2Resolving a bearing into components
• 3Bearings with a right angle
• 4Bearing of the return journey
• 5Bearing from a compass direction
• 6Finding a distance from two bearings
• 7Bearings from angle facts in an isosceles triangle
• 8Closest approach to a lighthouse
• 9Fixing a ship's position from two stations
• 10Back bearings with algebra
• 11Measuring a bearing and locating a point on a map
• 12A triangular sailing course: bearings, cosine rule and an obtuse angle

Worked examples (12)extended set

• 1Area from two sides and the included angle
• 2Finding a side from the area
• 3Finding an angle from the area
• 4Area from three sides
• 5Area rule in context
• 6Area of a quadrilateral
• 7Area of a parallelogram without a calculator
• 8A shaded region found by subtracting triangles
• 9Area of a regular octagon: show that, then work backwards
• 10Quadrilateral: find the diagonal, then the area
• 11Volume of a prism with a major-segment cross-section
• 12Area left unwatered by a sprinkler

Worked examples (11)extended set

• 1Finding a side with the sine rule
• 2Finding the third side
• 3Finding an angle with the sine rule
• 4The ambiguous case
• 5Choosing between the sine and cosine rules
• 6Sine rule in context
• 7Sine rule with exact values
• 8Sine rule twice across a quadrilateral
• 9Two positions of a hinged rod
• 10Show that an angle is correct to 1 decimal place
• 11A fenced plot with an obtuse angle

Worked examples (12)extended set

• 1Finding a side with the cosine rule
• 2Finding an angle from three sides
• 3Choosing which rule to start with
• 4Area of a triangle
• 5Cosine rule in context
• 6Working backwards to an unknown side
• 7Spotting a sign error with an obtuse angle
• 8Cosine rule without a calculator in a quadrilateral
• 9Overlapping sprinkler circles
• 10Show that a length is correct to 1 decimal place
• 11Edging a four-sided flower bed
• 12Angle of depression between the tops of two towers

Worked examples (9)extended set

• 1Key features of y = sin x
• 2Comparing sine and cosine
• 3The tangent graph and its asymptotes
• 4Reading solutions from a graph
• 5Sketch y = sin x, then use it to solve an equation
• 6Exact values and symmetry without a calculator
• 7Reading intersections and inequalities from two graphs
• 8Using one graph to solve several equations
• 9Where tan x meets 2 sin x: read, check and compare

Worked examples (11)extended set

• 1Solving a sine equation without a calculator
• 2Solving a cosine equation with a negative value
• 3Solving a tangent equation
• 4Equation needing rearrangement first
• 5Quadratic in sin x
• 6Rearranging with a negative coefficient, checked by a sketch
• 7A negative tangent: when the calculator's angle is out of range
• 8Spotting the lost negative root
• 9How many solutions? Reasoning with a horizontal line
• 10A tangent equation, then angles on a straight line
• 11A sine equation with a negative value

Worked examples (11)extended set

• 1Space diagonal of a cuboid
• 2Angle between a diagonal and the base
• 3Slant height of a pyramid
• 4Slant edge of a pyramid
• 5Angle between a slant edge and the base
• 6Angles in a cone
• 7Angle between a line and the base of a wedge
• 8Angles of elevation of a mast from a rectangular field
• 9Rectangular-based pyramid: show that, then compare two slopes
• 10Angle of depression between the tops of two masts
• 11Space diagonal of a cuboid given only its proportions