This review sheet contains all the information that you should remember from trigonometry.

Figure 1 is the unit circle with angles (given in degrees and radians) that will be frequently used in future courses. (All angles are stated in positive rotation.)

figure 1

Angular Velocity:

Arc Length:

s = r ´ x where x is in radians.

Here are the six basic trig functions based on the following reference triangle. (See figure 2)

figure 2

Here are the three special triangles that you should know. (See figure 3)

figure 3

 Here is a table of trig values that you should know.

DEG

0^o

30^o

45⁰

60^o

90^o

180^o

270^o

360^o

RAD

0

p

2p

Sin q

0

1

0

-1

0

Cos q

1

0

-1

0

1

Tan q

0

1

Und

0

Und

0

Cot q

Und

1

0

Und

0

Und

Sec q

1

2

Und

-1

Und

1

Csc q

und

2

1

Und

-1

Und

sin ² x + cos ² x = 1

tan ² x + 1 = sec ² x

cot ² x + 1 = csc ² x

cos (2a) = cos ² a - sin ² a = 2cos ² a - 1 = 1 - 2sin ² a

sin (2a) = 2sin a cos a

cos a cos b = [cos (a + b) + cos (a - b)]/2

cos a sin b = [sin (a + b) - sin (a - b)]/2

sin a cos b = [sin (a + b) + sin (a - b)]/2

sin a sin b = [cos (a - b) - cos (a + b)]/2

Here is a summary of the domains, ranges, periods of the sine, cosine, and tangent functions.

 f (x) = sin x

DOMAIN:

(-¥ , ¥ )

RANGE:

[-1, 1]

PERIOD:

2p

f (x) = cos x

DOMAIN:

(-¥ , ¥ )

RANGE:

[-1, 1]

PERIOD:

2p

f (x) = tan x

DOMAIN:

RANGE:

(-¥ , ¥ )

PERIOD:

p