1. Unit 9
Basic Trig

2. Today we will…
Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.

3. New Words
Trigonometry:
the study of the properties of triangles.
Trigonometric ratio:
ratio of the measures of 2 sides of a triangle.

4. New Words
Sine: written sin, read [sahyn]
Cosine: written cos, read [koh-sahyn]
Tangent: written tan, read [tan- juhnt)

5. New sayings Some old horse, caught another horse, taking oats away.
Signs of happiness come after having tankards of ale.
Some of her children are having trouble over algebra.
Some out houses can actually have totally odorless aromas.
SOH CAH TOA (read soh-kuh-toh-uh)

6. Right Triangle Has 3 sides: Hypotenuse
Adjacent
Opposite
The Hypotenuse is always across from the right angle. It is the longest.
The other two will depend on what angle we are dealing with

7. Right Triangle
The opposite side is across the triangle from the angle.
The adjacent side is next to the angle. It is one of the sides of the angle.

8. Right Triangle Hypotenuse Adjacent Opposite
If we are talking about this angle then...

9. Right Triangle Hypotenuse Adjacent Opposite
If we are talking about this angle then...

10. Sine
Sine is the ratio of the opposite side divided by the hypotenuse. C
opp
hyp 3 5
sin B = 5 3
opp
hyp 4 5
sin C = B 4

11. Cosine
Cosine is the ratio of the adjacent side divided by the hypotenuse. C
adj
hyp 4 5
cos B = 5 3
adj
hyp 3 5
cos C = B 4

12. Tangent C opp 3 adj tan B = 4 5 3 opp 4 adj tan C = 3 B 4
tangent is the ratio of the opposite side divided by the adjacent. C
opp
adj 3 4
tan B = 5 3
opp
adj 4 3
tan C = B 4

13. What’s up with the sayings
Some old horse, caught another horse, taking oats away.
opp
hyp
adj
hyp
opp
adj
sin =
cos =
tan =

14. Which ever one you like...
Some old horse, caught another horse, taking oats away.
Signs of happiness come after having tankards of ale.
Some of her children are having trouble over algebra.
Some out houses can actually have totally odorless aromas.
SOH CAH TOA (read soh-kuh-toh-uh)
soak-a-toe-a

15. New Words
Angle of
depression
elevation

16. Find tan j l 6 j
opp
adj 3 6
tan J = 3 45 k

17. Find cos j l 6 j
adj
hyp 6 45
cos J = 3 45
now simplify k

18. Find tan k l 12 j
opp
adj 12 5
tan K = 5 13 k

19. Find sin k l 12 j
opp
hyp 12 13
sin K = 5 13 k

20. Find cos k l 12 j
adj
hyp 5 13
cos K = 5 13 k

21. To find a side... 30 opp adj ? 13 13 tan 30 = ? 13 .5774 = ?
What ratio can we use?
What sides are we using? 30
opp
adj ? 13 13
tan 30 = ? 13
.5774 = ?
.5774 X 13 = ?

22. To find a side... 18 210 adj hyp ? 210 ? cos 18 = ? 210 .9511 =
What ratio can we use?
What sides are we using? 18
210
adj
hyp ?
210 ?
cos 18 = ?
210
.9511 =
.9511 X 210 = ?

23. To find an angle... 95 opp adj 95 40 tan ? = = 2.375 ? tan-1 2.375
What ratio can we use?
What sides are we using? 95
opp
adj 95 40
tan ? =
= 2.375 ?
tan
= 67.17 40

24. To find an angle... ? 3078 opp hyp 600 3078 sin ? = = .1949
What ratio can we use? ?
What sides are we using?
3078
opp
hyp
600
3078
sin ? =
= .1949
sin
= 11.24
600

25. Make sure your calculator is in degrees not radians
When calculating trig functions, round to 4 decimal places