DO NOT USE CALCULATORS FOR THIS WHOLE CLASS ACTIVITY.
YOU NEED TO KNOW: that the cosine and sine functions for ALL ANGLES are given by the coordinates of points on the UNIT CIRCLE. The x-coordinates of points on the unit circle give the cosine of the angle between the x-axis and the radius measured anti-clockwise […]
The Cape Town cable car takes tourists to the top of Table Mountain. The cable is 1.2 kilometres in length and makes an angle of 40 degrees with the ground. Calculate the vertical height (h) climbed by the cable car.
If the lower cable car station is 3o2 metres above sea level, […]
What does Pythagoras Theorem tell you about these angles?
Use this information to find this sum of squares of sines:
Many thanks to NRICH for this problem.
How could I make graph 2 from graph 1? Can you work out the equation of graph 2?
Graph 3 has equation y=sin2x. […]
Two ships are heading towards a lighthouse on the same path, one behind the other. From a height of 42 metre the closer ship is observed at an angle of depression θ where tan θ = ⅘ and the other ship at an angle of depression of 30 degrees. Draw a diagram.
A climber is stuck on a cliff face. A rescue worker on the ground is 200 m from the bottom of the cliff. The angles of elevation of the climber and of the top of the cliff as seen by the rescuer are 45 degrees and 60 degrees respectively. Draw a diagram.
Angles A, B and C are the angles of a triangle. Decide whether each of the following is an identity, always true for all triangles, or an equation, sometimes true. If you decide it is an equation find the solution or solutions and describe the corresponding triangle.
Click here for Notes for Teachers
The angle of elevation from a point C on the ground, at the centre of the goalpost, to the highest point A of the arc, directly above the centre of the Moses Madhiba Soccer Stadium in Cape Town, is 64.75 degrees. The soccer pitch is 100 metres long (PQ […]
The line RS is a tangent at P to the circle centre O and radius 1 unit.
Find the lengths OQ, PQ, PS, OS, OR and RP.
If OS and OR lie on the coordinate axes, what are the coordinates […]
How many ways can you prove that a + b = c?
What other interesting properties can you find?