TANGENTS, SINES, AND COSINES

What you need to know.

Review

To find the length of a side using the tan button on your calculator: Type in the measurement of the adjacent side,

then hit the TAN button, then type in the degree measurement of the angle. Hit enter.

EX: Type in:45 70◦ 45TAN70=

XYou should get 123.6364839 round to the nearest

tenth, so 123.6

What about those tangent ratios we did?

When do you use that ratio? When you need to find an angle measurement.

EX: C 403 TANA= 403/685

B A 685

To find the degree measurement of angle A, type in your calculator: 2nd TAN 403/685 ENTER.

You should get 30.46920015. Round to the nearest tenth, so 30.5 is the measure of angle A, or TANA=30.5.

You try:

What is the degree measurement of angle F, or TANF?

D

12ft

E F16ft

Answer

You should have entered into your calculator 2nd TAN 12/16 ENTER and the answer you should have is 36.9

Try again:

What is the degree measurement of angle D, or TAND?

D

12ft

E F16ft

Answer

You should have entered into your calculator:

2nd TAN 16/12 ENTER.The answer you should have is 53.1.

What you are doing here is using the inverse tangent function. Big words you need to remember.

Assignment

PAGE 568 8-17 You have 20 minutes to do

this and turn it in! I am grading this!!!

SINE and COSINEFormulas you need to know:SINE: leg opposite COSINE: leg

adjacent hypotenuse

hypotenuseSine and Cosine are used when you have one

leg measurement and the hypotenuse measurement and you need the angle measurement.

Depending on the information you have, you use sine or cosine.

Example:

BLeg opposite hypotenuse angle ALeg adjacent angle B

C leg opposite B Aleg adjacent A

SINA=BC SINB= AC AB AB

COSA = AC COSB= BC AB AB

Example:

SINA: 7/12COSA: 10/12SINB: 10/12COSB: 7/10

7

B

CA

12

10

Notice anything? The Sines and Cosines of one angle are exactly opposite of the Sines and Cosines of the other angle. Hmm.

These are called sine ratios and cosine ratios, Like the tangent ratios we did Friday.

You try:

SINR:COSR:SINP:COSP:

P

Q R

5

13

Answers:SINR: 5/13COSR: 13/5SINP: 13/5COSP: 5/13

What if you know the length of the hypotenuse and the measurement of the angle, but you need to measurement of the leg?

Enter into your calculator:

Measure of the hypotenuse SIN 20 Enter

Or 8395SIN20=You should get 2871.3

feet.

20

B

C A

8395ft

20

You try:Fine the

measurement of BC.

20

B

C A

72 m

15

Answer:You should have

entered into your calculator:

72SIN15=

The answer: 18.6 m

20

B

C A

72 m

15

Assignment:Page 576 12-29 all

You have to turn this in!!! If you do not finish in class, this is homework-it is due at the

beginning of class tomorrow-I WILL GRADE THIS BEFORE WE GO OVER IT!!!!!!!