x

y

5

4

Find the exact trig values for an angle of 5

4

This angle has a terminal side in the 2nd quadrant (because 5/4 = 1.2)

5

4ref angle

4

ref angle

2sin

2 2

cos2

tan 1

Finding Trig Values from an x-y coordinate

x

y

( 5, 3)

Find the 6 trig functions for an angle which has terminal side passing through (-5, -3)

3

5

34 3tan

5

34csc

5

34sec

3

5cot

3

2 2 2a b c 2 2 23 5 c

234 c34 c

5 34sin

34

3 34cos

34

x

y

Find the for all angles that are between 0 and 360 degrees (also in include the radian measurements

1 3sin

2

From the chart we get that 60 degrees has a

sin is negative in the 3rd and 4th quadrants

60 3

ref angle or

45

4180 60 240 or

3

3sin

2

5360 60 300 or

3

Law of Cosines – Solve the TriangleA

C

B

34

23

2 2 2 2 cosb a c ac B

Solve the triangle

2 2 215 34 23 2(34)(23)cos( )B 225 1156 529 1564cosB

225 1685 1564cosB

15

Law of Cosines – Solve the TriangleA

C

B

34

23

Solve the triangle

225 1685 1564cosB 15

168516851460 1564cosB

15641564.9335 cosBarccos(.9335)

21B

Law of Cosines – Solve the TriangleA

C

B=21º

34

23

Solve the triangle15

23*sin 21 15*sinC8.2424 15sinC

15

sin sinB C

b c

sin 21 sin

15 23

C

15.5495 sinCarcsin(.5495)

33C

Law of Cosines – Solve the TriangleA

C=33º

B=21º

34

23

Solve the triangle15

180 33 21 A 126 A

Law of Cosines – Solving a TriangleC

A

B

75º1443

2 2 2 2 cosc a b ab C

Find missing side of the triangle, and then use the law of sines to find the missing angles

2 2 214 43 2(14)(43)cos(75)x 2 196 1849 311.62x

2 1733.38x 41.63x

41.63

Law of Cosines – Solving a TriangleC

A

B

75º1443

Find missing side of the triangle, and then use the law of sines to find the missing angles

sin sinC B

C B

41.63 We can now use law of sines to find one of the angles that is missing

sin 75 sin

41.63 14

B

Law of Cosines – Solving a TriangleC

A

B

75º1443

sin sinC B

C B

41.63sin 75 sin

41.63 14

B

41.63*sin 14*sin 75B 41.63*sin 13.52B

41.63 41.63sin .3248B

1sin (.3248)

18.95B

Law of Cosines – Solving a TriangleC

A

B

75º1443

41.63

18.95B

Now use this angle and the 75 that you were given in the beginning to find the 3rd angle

180 75 18.95 86.05

86.05C

727 #1-3 (sketch the angles and reference angles – then find the answers)

727 #4-6 (find all angles between 0 and 360 and their radian counterparts)

724 #75, 79 (find all missing angles and show ALL work along with a drawing)

724 #81 (find all missing sides and angles – DO NOT FIND AREA)

697 #9, 11, 13, 15 (make sure they have the proper signs and show ALL work)697 #22, 23, 25, 27 (sketch and find the

reference angle)697 #36, 38, 40 (you need a sketch and to

explain how you know without using the calculator)