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## Grade 10 General Angle Trigonometry Investigation

*By toni On 27 September, 2017 · Leave a Comment*

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 […]

## Grade 10 Cable car

*By toni On 20 September, 2017 · Leave a Comment*

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, […]

## Grades 11 and 12 Degree Ceremony

*By toni On 19 July, 2017 · Leave a Comment*

Draw a triangle with angles x, (45 + x) and (45 – x) degrees.

What does Pythagoras Theorem tell you about these angles?

Use this information to find this sum of squares of sines:

See the AIMSSEC Notes for Teachers.

Many thanks to NRICH for this problem.

## Grades 10 to 12 Tangled Trig Graphs

*By toni On 17 July, 2017 · Leave a Comment*

Graph 1 is the graph y=sinx. Can you identify the coordinates of the points where it crosses the axes and where it reaches its maximum and its minimum values?

How could I make graph 2 from graph 1? Can you work out the equation of graph 2?

Graph 3 has equation y=sin2x. […]

## Grades 10 and 11 At Sea

*By toni On 17 July, 2017 · Leave a Comment*

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.

[…]

## Grades 10 and 11 Cliff Rescue

*By toni On 17 July, 2017 · Leave a Comment*

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.

[…]

## Grades 11 and 12 Always or sometimes

*By toni On 20 May, 2017 · Leave a Comment*

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

## GRADE 12 IN A SOCCER STADIUM

*By toni On 30 April, 2017 · Leave a Comment*

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 […]

## Grades 10 to 12 Trig Lengths

*By toni On 23 July, 2016 · Leave a Comment*

In the diagram the line OS is perpendicular to the lines OR and 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 […]

## Grades 10 to 12 Three By One

*By toni On 1 June, 2016 · 2 Comments*

This rectangle measures three units by one unit. The diagram shows three angles a, b and c.

How many ways can you prove that a + b = c?

What other interesting properties can you find?

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