### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# DIFF CALC THRY MATH 2400

UGA

GPA 3.56

### View Full Document

## 12

## 0

## Popular in Course

## Popular in Mathematics (M)

This 2 page Class Notes was uploaded by Joanne Bergnaum on Saturday September 12, 2015. The Class Notes belongs to MATH 2400 at University of Georgia taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/202083/math-2400-university-of-georgia in Mathematics (M) at University of Georgia.

## Reviews for DIFF CALC THRY

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/12/15

Trigonometry New and Old 24 MATH 00H Fall 2006 De nitions 7 cos 9 7 sin 9 y r r y x r 0050 S600 I r x tang X ctn0 i x y Note that cos and sec are even functions whereas sin tan csc and cot are odd functions The basic relations are of course based on the Pythagorean Theorem sin2 0 cos2 0 1 tan2 0 1 2 sec2 0 1 cot2 0 csc2 0 Note also that sin 2 ox cos oz cos72 ox sin oz sin7 ox sin oz and cos7 ox cos a Area The area of a triangle is A bh If two sides a and b and the included angle 0 of a triangle are given then we take 17 as the base and the height is h a sin 0 so a 19 Addition Formulas We begin with T lsinot8 sinotcos cosotsin Consider the diagram at the right Here points D and E resp are obtained by dropping perpendiculars from B and A resp onto 0C It follows that AACE E ABCD and so Thus AECD BDCE from which we conclude that areaAACD areaABCE Now using this result we have1 sinot 8 2areaAOAB 2areaAOAC areaAOCB 2areaAOAD areaAOEB sinot cos8 COSOt sin 1This proof was inspired by a suggestion of Dr Mark Faucette at the University of West Georgia By substituting 8 for 8 in T and using the symmetries of the respective functions we obtain lsinot 8 sinotcos9 cosotsin8 Similarly substituting l at for at in T we obtain lcosot8 cosotcos9 qsinotsin8 As a consequence we have the double angle formulas 2 2 ot sin a2cos2a 11 2sin2a sin2a 2sinotcosot Law of Cosines In AABC let 0 be the length of the side opposite angle 0 Then 02a2b2 2abcos0 A The easiest proof is to assign cartesian coordinates to the points A B and C Let C 00 B a 0 and A b cos0 bsin0 Then we infer from the distance formula that lcos 205 cos 02 a bcos02 bsin02 a2 172 2abcos0 Law of Sines In AABC let the sides a b c be opposite the angles oz 8 y respectively Then sin oz sin 8 sin y a b c We ll establish only the rst equality here Drop a perpendicular from C to E as indicated in the diagram Then I I hbsinaasin gt wz a b as desired Basic Limits Recall that the area of the unit circle is by de nition 7 and so the area of a sector with central angle 0 is 7 0 From the gure at the right 7 we see rst that areaAOAC 5 areasector0AC and so sin0 5 0

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "I made $350 in just two days after posting my first study guide."

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.