Geo 6.4 6.5

MODERN GEOMETRYSections 6.4, 6.5

Thompson

ANNOUNCEMENTS

Exam III on Tuesday 3/24

Covers Chapters 2 - 6

TEACHING PROJECT

Hippocrates’ Quadrature of the Lune (440 B.C.)

Euclid’s Proof of the Pythagorean Theorem (300 B.C.)

Archimedes Determination of Circular Area (225 B.C.)

Heron’s Formula for Triangular Area (75 A.D)

A Gem from Isaac Newton (1665)

TANGENT RATIO

SINE, COSINE RATIO

TRIGONOMETRIC RATIOS

hyp

oppsin

hyp

adjcos

adj

opptan

opp

hyp

sin

1csc

adj

hyp

cos

1sec

opp

adj

tan

1cot

cos

sintan

THE UNIT CIRCLE

FINDING TRIG RATIOS

3

4

5

FINDING UNKNOWN ANGLES

3

4

5

“SOLVING” RIGHT TRIANGLES

a

b

14

43

FINDING AREA

A

B

cm35

50C

cm75

FORMULAS & IDENTITIES

Reciprocal Identities

Pythagorean Identities

1cossin 22

SOLVING OBLIQUE (NON-RIGHT) TRIANGLES

THE LAW OF SINES

Use Law of Sines when given:

•An angle and its opposite side.

•Any two angles and one side.

•Two sides and the non-included

angle.

THE LAW OF COSINES

Use Law of Cosines when given:

•Two sides and the included angle.

•All three sides.

SOLVE THE TRIANGLE

SOLVE THE TRIANGLE

SOLVE THE TRIANGLE

SOLVE THE TRIANGLE

SOLVE THE TRIANGLE

SOLVE THE TRIANGLE

CIRCLE TRIG!

PYTHAGOREAN IDENTITIES

CLASSWORK / HOMEWORK

6.4

27, 45, 49, 67, 69

6.5

33, 35, 39, 47