Geom trig packet of worksheets PDF

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Trigonometry of the Right Triangle - 1 In your study of trigonometry of the right triangle, you will discover ways in which the similarity of triangles will provide additional methods for measuring segments and angles indirectly.

G Three right triangles are drawn to coincide at vertex A. Since each triangle contains a right angle as well as , we know that all . three triangles are similar by AA

E C

Also, since corresponding sides of similar triangles are in proportion, we can say:

F

D

B

Let’s recall our Trigonometric Ratios….. Remember “SOH CAH TOA”

Sine

Cosine cos

sin

Tangent tan

Reciprocal Functions

Cosecant csc

Secant sec

Cotangent cot

A

1. Evaluate the six trigonometric functions of the given angle: (EXACT value)

G E C 15

10

6

9

5 3

A

F

A

D

A

B 4

8

12

sin A

sin A

sin A

cos A

cos A

cos A

tan A

tan A

tan A

csc A

csc A

csc A

sec A

sec A

sec A

cot A

cot A

cot A

2. Find the value. (Use your CALCULATOR. Round to the nearest thousandth, if necessary) a.

tan 24

d. sec 72

b. sin 30

c. cos55

e. cot 52

f. csc 40

3. Given right

below, find the EXACT value of:

4. Given right

below, tan A

9 find the EXACT 12

value of: K

B

a. sin L =

a. csc A =

17

b. sec L =

15

b. cot A =

L

J

A

C

c. tan K =

8

c. cos B =

Trigonometric Values for Special Angles

30o - 60o - 90o

45o - 45o - 90o

60°

45°

2x

x 2

1x

x 30°

45°

x 3

x

5. Find the EXACT value of the trigonometric functions:

sin 30

sin 60

sin 45

cos 30

cos 60

cos 45

tan 30

tan 60

tan 45

csc 30

csc 60

csc 45

sec 30

sec 60

sec 45

cot 30

cot 60

cot 45

6. Evaluate the six trigonometric functions of the given angle: (EXACT value)

B

B a.

b. 60°

45° 14

7 2 16

8

45°

30°

C

C

A

8 3

sin 30

sin 60

sin 45

cos 30

cos 60

cos 45

tan 30

tan 60

tan 45

7 2

7. Find the measure of the given angle: *Use your trigonometric values of special angles*

a.

B

b.

B x 8 2

16

10 5 x

C

m

A

C

m

A

A

Trigonometry – Worksheet 1 1. Find the exact value of the six trigonometric functions of the given

x.

sin x cos x

15

x

tan x

7 csc x sec x cot x

2. Let x be an acute angle of a right triangle. Find the values of the other 5 trigonometric functions of x, if 13 . sec x 5

x

3. Given right

sin x

csc x

cos x

sec x

tan x

cot x

below, find the EXACT value of:

C

a. cos C =

5

b. csc C =

3 c. tan A =

B

A 4

d. sec A =

4. Find the value. (Use your CALCULATOR. Round to the nearest thousandth, if necessary)

a.

sec 24

b. tan 70

c. csc 55

5. If one side of an equilateral triangle has a length of 6, what is the length of its altitude? Show work.

6. Find the measure of the given angle: *Use your trigonometric values of special angles*

a. x

10

5 3

4 2 b.

x 4 2

7. Can the sin x ever be a value greater than 1? Explain.

Unit Circle Worksheet A

Name__________________ Period____________

Solve the following problems using your Unit Circle. 1)

sin(90 )

2) cos

3) sin

 4) cos 135

5) tan

6) tan(180 )

7) sin

8) cos





Unit Circle Worksheet B

Name__________________ Period____________

Solve the following problems using your Unit Circle. 1)

sin(150  )

2) cos



3) sin

4) cos

5) tan

6) tan(135 )

7) sin

8) cos





Unit Circle Worksheet C

Name___________________ Period___________

The given point P is located on the Unit Circle. State the quadrant and find the angle , also sin , cos and tan . 1) P

2) P(0,

3)P

Quad:

Quad:

Quad:

sin :

sin :

sin :

cos :

cos :

cos :

tan :

tan :

tan :

Find the exact value of each function. 4) cos

5) sin

7) cos(600 )

8) sin

10) cos

11) sin

13) cos(1440 )

14) sin

6) sin



9) tan(7



12) tan(585 )

15) cos

M126 Worksheet 6.1 - Inverse Circular Functions 1)

Name__________________________ _

Find the exact value of the real number y. a) y = sin-1

3 2

b)

y = arcsec (1)

c) y = arctan 1

2)

Use a calculator to give the value to the nearest degree. a) θ = cos-1(.8910) b) θ = tan-1 (2.2460)

3)

Use a calculator to give the real number value. a) y = sin-1(-.4848)

4)

Evaluate the expression. a) arccos cos

5)

c) y = cot-1 (2.5181552)

b) y = arcsec (2.8842912)

π 2

u Write tan cos-1 3

b) cos arcsin

1 4

as an algebraic expression in u, u > 0.

1...