Announcements

• Test Friday, material through 6.2 (today)

• Sample test posted

• Bring picture ID

• You can use the Windows calculator, your own calculator, or the grapher from Lab 2.

• You can’t use the book, your notes, online notes, email, or AIM

A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called the hypotenuse, and the remaining two sides are called the legs of the triangle.

cb

a

90

Initial side

Terminal side

a

bc

The six ratios of a right triangle are called trigonometric functions of acute angles and are defined as follows:

sine of

cosine of

tangent of

cosecant of

secant of

cotangent of

Function namesin

cos

tan

csc

sec

cot

Abbreviation Valueb c

a c

b a

c b

c a

a b

/

/

/

/

/

/

Find the value of each of the six trigonometric functions of the angle .

Adjacent

12 13

c = Hypotenuse = 13

b = Opposite = 12a b c2 2 2

a2 2 212 13

a2 169 144 25 a 5

a

b

c

Adjacent = 5

Opposite =

Hypotenuse =

12

13

sin OppositeHypotenuse

1213

cos AdjacentHypotenuse

513

tan OppositeAdjacent

125

csc HypotenuseOpposite

1312

sec HypotenuseAdacent

135

cot AdjacentOpposite

512

b a c2 2 2

cb

a

90

b

c

a

c

c

c

2

2

2

2

2

2

bc

ac

2 2

1

sin cos2 2 1

Theorem Complementary Angles Theorem

Cofunctions of complementary angles are equal.