8-4Sine, Cosine, and Tangent Ratios

Chapter 8 Section 4

Mrs. Brook

Vocabulary

Trigonometry

Derived from Greek words meaning “triangle measurement”

Triangle terminology

Opposite side: the side opposite the angle

angle

angle

angle

op

posite

opposite

op

posite

oppositeangle

Adjacent side: the side beside the angle

adjacent

adjacent

ad

jace

nt

ad

jace

nt

angle

angle

angle

angle

Hypotenuse: the longest side and across from the right angle

hypotenuse

hypotenuse

hypotenuse

hypotenuse

SOH CAH TOA

SOH

CAH

TOA

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

Definitions

A

B

90o

C

ac

b

Sine of angle A

A

B

90o

C

ac

b

sin(A) = =ac

oppositehypotenuse

Sine of angle B

A

B

90o

C

ac

b

sin(B) = =bc

oppositehypotenuse

Cosine of angle A

A

B

90o

C

ac

b

cos(A) = =bc

adjacenthypotenuse

Cosine of angle B

A

B

90o

C

ac

b

cos(B) = =ac

adjacenthypotenuse

Tangent of angle A

A

B

90o

C

ac

b

tan(A) =oppositeadjacent

ab

=

Tangent of angle B

A

B

90o

C

ac

b

tan(B) =oppositeadjacent

ba

=

Write the Sin, Cos, and Tan Ratios for angle A

A

BC7

2425

SOH CAH TOA

Sin A = 7/25

Cos A = 24/25

Tan A = 7/24

Try this one

Sin E

Cos E

Tan E

Sin F

Cos F

Tan F

SOH CAH TOA

6/10 = 3/5

8/10 = 4/5

6/8 = 3/4

8/10 = 4/5

6/10 = 3/5

8/6 = 4/3

Find the value of x using Trig.Note: If “x” is on top - multiply; If “x” is on bottom - divide!!

647

X------

THIS IS JUST THE ANGLE!!

Remember: SOH CAH TOA

Since we have anO & A we use Tan(no hypotenuse!)

Tan 64 = x/7

Since x is on top, mult.Type 7 * tan 64 in calc.

67x

6------

35----

X20

6250

------x

Since we have anO & A we use Tan(no hypotenuse!)

Tan 67 = 6/x

Since we have anO & H we use Sin

Sin 35 = x/20

Since we have anA & H we use Cos

Cox 62 = 50/x

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 divideType 50 divided by cos 62in calc.

Find the value of x degrees using Trig. Note: When finding an angle measure use “inverse” Trig. or

the 2nd button!!

x39____

x16-----20

x____45

Remember: SOH CAH TOA

Since we have anO & A we use Tan(no hypotenuse!)

Tan x = 9/3

Since we have anA & H we use Cos

Cos x = 16/20

Since we have anO & H we use Sin

Sin x = 4/5

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.

Since x is the angle, use the 2nd button!Type 2nd Sin, then 4/5 using the n/d button.

71.6 36.9 53.1

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

Here’s your daily joke

Why didn’t sin and tan go to the party?

Just cos Ha! Ha!