1. The Primary Trigonometric Ratios
Trigonometry: The study of triangles (sides and angles)
Trigonometry has been used for centuries in the study of:
surveying
astronomy
geography
engineering
physics

2. Parts of a Right TriangleB
hypotenuse
opposite A C
adjacent

3. B
hypotenuse
adjacent
opposite C A

4. B
hypotenuse
opposite A
adjacent C

5. B
hypotenuse
adjacent C A
opposite

6. B
hyp
opp A C
adj
SOH
CAH
TOA

7. SOH
CAH
TOA B
hyp 10
opp 8 A C 6
adj

8. B
hyp
SOH
CAH
TOA 5
adj 3 A C 4
opp

9. SOH
CAH
TOA B
hyp 13 5
adj A 12 C
opp

10. Use a calculator to determine the following ratios.
sin 21° =
0.3584
cos 53° =
0.6018
tan 72° =
3.0777

11. sin A = 0.4142 ÐA = sin-1(0.4142) = 24° cos B = 0.6820
Determine the following angles (nearest degree).
sin A =
ÐA = sin-1(0.4142)
= 24°
cos B =
ÐB = cos-1(0.6820)
= 47°
tan C = 1.562
ÐC = tan-1(1.562)
= 57°

12. Determine the following angles (nearest degree).
sin A =
ÐA = sin-1(0.5833)
= 36° =
cos B =
ÐB = cos-1(0.2666)
= 75° =
ÐC = tan-1(1.875)
tan C =
= 62°
= 1.875

13. a = 6 sin 30° a = 6 (0.5) a = 3 cm B Example 1: Determine side a opp
hyp
SOH
CAH
TOA
6 cm a
30º A C
a = 6 sin 30°
a = 6 (0.5)
a = 3 cm

14. Ex. 2: Name two trig ratios that will allow us to calculate side b.
50º
9 m
40º A b C

15. Example 3: Determine side b
SOH
CAH
TOA
55º
8 cm
adj A b C
opp
b = 8 tan 55°
b = 8 (1.428)
b = 11.4 cm

16. Example 4: Determine the measure of ÐP.
SOH
CAH
TOA R
adjacent
cos P =
12 cm
ÐP = cos–1( ) Q
17 cm
ÐP = 45.1° P
hypotenuse

17. Example 5: Determine the measure of side PR.
Method 1
adj
opp R q
12 cm
q(tan 35°) = 12
35° P Q
q = 17.1 cm

18. q = 17.1 cm Example 6: Determine the measure of side PR. Method 2 adj
opp R
ÐQ = 90° – 35° q
ÐQ = 55°
12 cm
35°
55° P Q
q = 12(tan 55°)
q = 12(1.428)
q = 17.1 cm

19. Ex. 7: In DPQR, ÐQ = 90°. 8 cm b) Find cos R . 4 cm R
a) Find sin R if PR = 8 cm and PQ = 4 cm. R P Q
8 cm
b) Find cos R .
4 cm
RQ2 = 82 – 42
RQ2 = 64 – 16
RQ2 = 48