M4.3.4 For the adult
Sine, cosine and tangent
A ladder 5 m long leans on a wall at 75° to the ground. How high up the wall does it reach?
What this chapter teaches
Sine, cosine and tangent are three fixed ratios of the sides of a right angled triangle, one for each angle. The learner labels the sides opposite, adjacent and hypotenuse, picks the ratio that uses the known side and the wanted side, then solves for the missing side. The calculator must be in degrees mode.
Three questions to ask
There is no one right wording. Listen for the idea.
- Which two sides does the ratio need, and how do you pick sin, cos or tan?
- When do you multiply by the ratio and when do you divide by it?
- What does the calculator show if it is in radians mode, and how can you tell?
After the chapter, the learner can
- Choose sin, cos or tan from the sides you know
- Use sin, cos or tan to find a missing side
What they copy into their notebook
SOH CAH TOA: sin = O ÷ H, cos = A ÷ H, tan = O ÷ A. Label O, A, H. Pick the ratio with your two sides. Unknown on top: multiply. Unknown below: divide.