1. 5.1 Trigonometric ratios of acute triangle

2. SOH CAH TOA

3. Example 1
Use the primary trig ratios to solve DEF. Round all answers to the nearest tenth.

4. Example 1
Use the primary trig ratios to solve DEF. Round all answers to the nearest tenth.

5. Example 2
The angle of depression from the top of a cliff to a boat is 12°.
If the boat is 138 m from the foot of the cliff, find the height of the cliff to the nearest tenth of a metre.

6. RECIPROCAL TRIGONOMETRIC RATIOS
cosecant (csc)
secant (sec)
cotangent (cot)

7. EXAMPLE 3
Determine the value of each of the following. Round to 4 decimal places.

8. Example 4
Determine the value of each of the following. Round to 4 decimal places. a) csc 53 b) sec 32 c) cot 84

9. Example 4
Determine the value of each of the following. Round to 4 decimal places. a) csc 53 = b) sec 32 = c) cot 84 =

10. Example 5
Determine the measure of the missing angle. Round to the nearest degree. a) csc  = 1.5 b) cot  = c) sec  =

11. Example 5
Determine the measure of the missing angle. Round to the nearest degree. a) csc  = 1.5  = 42o b) cot  =  = 11o c) sec  =  = 73o

12. Example 6
Find OP, to the nearest tenth of a metre. Use reciprocal trigonometric ratios.

13. INTERESTING OBSERVATIONS
sin  1 and cos   1
csc   1 and sec   1
tan   1 , tan  = 1 or tan   1
cot   1 , cot  = 1 or cot   1

14. WHY DO WE USE CSC, SEC & COT?

15. WHY DO WE USE CSC, SEC & COT?
unknown variable can be expressed in the numerator
making calculations easier

16. HOMEFUN 
pg # 1, 2, 3, 4, 5i, 5iv, 6, 7, 8, 11, 15, 16 Check out examples 1, 2, 3 on pg 276 – 279 (if needed)