1. Trigonometry - Sin, Cos or Tan...

2. Starter O T A Use Tan to find the missing angle in this triangle…
Opp Adj
Tanθ = θ
30.19º
Hyp
Tanθ =
16.5cm
Adj
Tanθ =
0.581…
θ =
Tan …
θ =
30.19º (2dp)
9.6cm
Opp

3. Trigonometry – Sin, Cos or Tan?
So far, we have looked at using Sin, Cos and Tan to find missing angles or sides in a right-angled triangle
Today we are going to decide which of the above 3 to use
This links into which 2 sides of the triangle are involved in the calculation

4. Trigonometry – Sin, Cos or Tan?H C A H T O A
Opposite and Hypotenuse
 use Sin
Adjacent and Hypotenuse
 use Cos
Opposite and Adjacent
 use Tan
“SOHCAHTOA”

5. Trigonometry – Sin, Cos or Tan?
Find the vertical height of the triangle…
We will be using the SOH triangle… S H C H T A
Hyp
12.5m
Opp =
Sinθ x Hyp
Height
Opp
Opp =
Sin42 x 12.5
42°
Opp =
8.36m (2dp)
Adj
Two sides involved  Opposite and Hypotenuse

6. Trigonometry – Sin, Cos or Tan?
Work out the side labelled ‘x’
We will be using the TOA triangle… S H C H T A
Adj x
34°
Opp Tanθ
Adj =
Opp
Hyp
2.3cm
2.3 Tan34
Adj =
Adj =
3.41cm (2dp)
Two sides involved  Adjacent and Opposite

7. Trigonometry – Sin, Cos or Tan?
Find the area of this triangle. Give your answer to 4sf.
We need to find the 2 missing sides… S H C H T A
Opp
Adjacent Side
Opposite Side
Adj =
Cosθ x Hyp
Opp =
Sinθ x Hyp
Adj
6.1m
64°
Hyp
Adj =
Cos64 x 6.1
Opp =
Sin64 x 6.1
Adj =
2.67m (2dp)
Opp =
5.48m (2dp)
Two sides involved  Adjacent and Hypotenuse
Two sides involved  Opposite and Hypotenuse
Area  (Opp x Adj) ÷ 2
 14.66m2 (4sf)

8. Summary We have continued our work on Trigonometry
We have now seen how to decide whether to use Sin, Cos or Tan
The decision is entirely based on which pair of sides we have…