1. 8-4 Sine, Cosine, and Tangent Ratios
Chapter 8 Section 4
Mrs. Brook 

2. Vocabulary Derived from Greek words meaning “triangle measurement”
Trigonometry

3. Triangle terminology

4. Opposite side: the side opposite the angle

5. Adjacent side: the side beside the angle

6. Hypotenuse: the longest side and across from the right angle

7. SOH CAH TOA
You need to memorize this!!! Use SOH CAH TOA to help you remember these ratios!!!
SOH
CAH
TOA

8. Definitions B c a A
90o C b

9. Sine of angle A
opposite
hypotenuse a c B
sin(A) = = c a A
90o C b

10. Sine of angle B
opposite
hypotenuse b c B
sin(B) = = c a A
90o C b

11. Cosine of angle A
adjacent
hypotenuse b c B
cos(A) = = c a A
90o C b

12. Cosine of angle B
adjacent
hypotenuse a c B
cos(B) = = c a A
90o C b

13. Tangent of angle A
opposite
adjacent a b B
tan(A) = = c a A
90o C b

14. Tangent of angle B
opposite
adjacent b a B
tan(B) = = c a A
90o C b

15. Write the Sin, Cos, and Tan Ratios for angle AB C 7 24 25
SOH CAH TOA
Sin A = 7/25
Cos A = 24/25
Tan A = 7/24

16. Try this one  Sin F Sin E Cos F Cos E Tan F Tan E SOH CAH TOA
6/10 = 3/5
8/10 = 4/5
6/8 = 3/4
Sin F
Cos F
Tan F
8/10 = 4/5
6/10 = 3/5
8/6 = 4/3
Sin E
Cos E
Tan E

17. Find the value of x using Trig.
Note: If “x” is on top - multiply; If “x” is on bottom - divide!!
Remember: SOH CAH TOA
THIS IS JUST THE ANGLE!!
Since we have an
A & H we use Cos
Cox 62 = 50/x
Since we have an
O & A we use Tan
(no hypotenuse!)
Tan 64 = x/7
Since we have an
O & A we use Tan
(no hypotenuse!)
Tan 67 = 6/x
Since we have an
O & H we use Sin
Sin 35 = x/20 64 7 X
------ 67 x 6
------ 35
---- X 20 62 50
------ x
Since x is on top, mult.
Type 7 * tan 64 in calc.
Since x is on bottom divide.
Type 6 divided by tan 67 in calc
Since x is on top, mult.
Type 20 * sin 35 in calc.
Since x is on bottom divide
Type 50 divided by cos 62
in calc.

18. Find the value of x degrees using Trig.
Note: When finding an angle measure use “inverse” Trig. or the 2nd button!!
Remember: SOH CAH TOA
Since we have an
O & A we use Tan
(no hypotenuse!)
Tan x = 9/3
Since we have an
A & H we use Cos
Cos x = 16/20
Since we have an
O & H we use Sin
Sin x = 4/5 x 3 9
____ x 16
----- 20 x
____ 4 5
71.6
36.9
53.1
Since x is the angle, use the 2nd button!
Type 2nd Sin, then 4/5 using the n/d button.
Since x is the angle, use the 2nd button!
Type 2nd Tan, then 9/3 using the n/d button.
Since x is the angle, use the 2nd button!
Type 2nd Cos, then 16/20 using the n/d button.

19. What have I learned? SOH CAH TOA If “x” is on bottom “divide”
If “x” is on top “multiply”
If solving for a side use regular sin, cos, or tan
If solving for an angle use inverse sin, cos, or tan

20. Here’s your daily joke 
Why didn’t sin and tan go to the party?
Just cos Ha! Ha! 