Lesson 2 - Introducing sine, cosine and tangent

In this lesson you will:

• learn why we need trigonometry

• practise identifying and labelling right-angled triangles and their sides

• discover the link between sin, cos and tan and the ratio of sides

• practise choosing which equation to use, SOH, CAH or TOA.

Task 1

• Watch the video, Boat Dock.

• Answer the following questions in your exercise book or folder:

  1. Which is the best ramp? Explain your reasoning.

  2. Which is the worst ramp? Explain your reasoning.

  3. What information would be helpful to figure out the best possible ramp length?

Task 2

Use the embedded Boat dock interactive to complete the activity.

Answer all the questions in your exercise book or folder.

1. Experiment with different length ramps until you come up with the ‘perfect ramp’.

2. Record details about your perfect ramp. Explain your reasoning.

3. There is an angle on the diagram that is shown to be constantly changing. Which angle is this measuring? Draw a diagram to illustrate this.

4. What is the angle when your ramp is at its steepest?

5. What is the angle when the ramp is at its flattest?

6. How does the length of your ramp affect this angle?

7. Research the steepness of wheelchair ramps. How does your ramp fit in with these recommendations? Adjust the length of your ramp if you need to.

Task

1. Use the embedded Geogebra app to change the angle in the triangle.

   • What do you notice?

   • What do you wonder?

   • What happens to the ratios as the angle gets larger?

   • What happens to the ratios as the angle gets smaller?

2. Keeping the reference angle the same, change the length of side AB.

   • What do you notice?

   • What do you wonder?

   • What happens to the ratios as the side increases?

   • What happens to the ratios as the side decreases?