1. Warm – up: Find the missing measures. Write all answers in radical form.
30°
45° x 7 10 z
45° w
60° y

2. The Trigonometric Functions we will be looking at
SINE
COSINE
TANGENT

3. The Trigonometric Functions
SINE
COSINE
TANGENT

4. SINE
Prounounced “sign”

5. Prounounced “co-sign”
COSINE
Prounounced “co-sign”

6. Prounounced “tan-gent”

7. Represents an unknown angle
Greek Letter q
Prounounced “theta”
Represents an unknown angle

8. hypotenuse
hypotenuse
opposite
opposite
adjacent
adjacent

9. We need a way to remember all of these ratios…

10. Some
Old
Hippie
Came A
Hoppin’
Through
Our
Old Hippie
Apartment

11. Sin
SOHCAHTOA
Opp
Hyp
Cos
Adj
Hyp
Tan
Opp
Adj
Old Hippie

12. Or maybe a video would be better….

13. Finding sin, cos, and tan Maybe this will help….

14. SOHCAHTOA 10 8 6

15. 10.8 9 A 6 Find the sine, the cosine, and the tangent of angle A.
Give a fraction and decimal answer (round to 4 places).
10.8 9 A 6

16. ? 5 4 3 Pythagorean Theorem: (3)² + (4)² = c² 5 = c
Find the values of the three trigonometric functions of . ?
Pythagorean Theorem: 5 4
(3)² + (4)² = c²
5 = c 3

17. 24.5 8.2 23.1 Find the sine, the cosine, and the tangent of angle A
Give a fraction and decimal answer (round to 4 decimal places). B
24.5
8.2 A
23.1

18. Word Problems…

19. Ex.
A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree?
tan 71.5° ?
tan 71.5°
71.5°
y = 50 (tan 71.5°) 50
y = 50 ( )

20. Ex. 5
A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge?
cos 60°
x (cos 60°) = 200
200
60° x x
X = 400 yards

21. To find the distance d from a house on shore to a house on an island, a surveyor measures the distance between points A and B as shown. Using an instrument called a transit, he finds the measurement of
What is the distance between the 2 houses?

22. What is the distance between the 2 houses?
To find the distance d from a house on shore to a house on an island, a surveyor measures the distance between points A and B as shown. Using an instrument called a transit, he finds the measurement of
What is the distance between the 2 houses?
SOLVE IT!
Draw a picture.
Label it with what you know.
Identify what you need to find.
Find the right triangle – (if there isn’t one, make one!).
Solve using right triangle trig. Ratios.

23. Solve the problem: