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 (SOH) (CAH)
(TOA)

9. What’s the purpose of SOH CAH TOA?
The Sine, Cosine and Tangent functions express the ratios of sides of a right triangle. We use this to find missing angles. We can find an unknown angle in a right-angled triangle, as long as we know the lengths of two of its sides. The function takes an angle and gives us the ratio, and the inverse function takes the ratio to give us the angle

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

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

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

13. Finding sin, cos, and tan

14. SOHCAHTOA
Sin = 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. Now, find the actual measurement of angle A by using the inverse
STOP: Make sure Mode on your calculator is set to “Degree” not “Radian”
24.5
8.2 B A
23.1
sin-1 (8.2/24.5)= 19.6 degrees
No matter how you do it, you should get the same answer (and because we have all 3 sides, it doesn’t matter which we choose)
cos-1 (23.1/24.5)= 19.5 degrees
tan-1 (8.2/23.1)= 19.5 degrees
Check: Does it make sense? Lets check Angle B:
sin-1 (23.1/24.5)= 70.5 degrees
= 180 degrees. That works!

19. Finding a side

20. Ex.
A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the non-right angle from the ground 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 ( )

21. Ex. 2
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