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TRIGONOMETRY. By Mindy Crall. Angles, Arc length, Conversions. Angle measured in standard position. Initial side is the positive x – axis which is fixed. Terminal side is the ray in quadrant II, which is free to rotate about the origin. Counterclockwise rotation

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trigonometry

TRIGONOMETRY

By Mindy Crall

angles arc length conversions
Angles, Arc length, Conversions

Angle measured in standard position.

Initial side is the positive x – axis which is fixed.

Terminal side is the ray in quadrant II, which is free

to rotate about the origin. Counterclockwise rotation

is positive, clockwise rotation is negative.

Coterminal Angles: Angles that have the same terminal side.

60°, 420°, and –300° are all coterminal.

Degrees to radians: Multiply angle by

Radians to degrees: Multiply angle by

Note: 1 revolution = 360° = 2π radians.

right triangle trig definitions
Right Triangle Trig Definitions

B

  • sin(A) = sine of A = opposite / hypotenuse = a/c
  • cos(A) = cosine of A = adjacent / hypotenuse = b/c
  • tan(A) = tangent of A = opposite / adjacent = a/b
  • csc(A) = cosecant of A = hypotenuse / opposite = c/a
  • sec(A) = secant of A = hypotenuse / adjacent = c/b
  • cot(A) = cotangent of A = adjacent / opposite = b/a

c

a

A

C

b

special right triangles
Special Right Triangles

30°

45°

2

1

60°

45°

1

1

basic trigonometric identities
Basic Trigonometric Identities

Quotient identities:

Even/Odd identities:

Even functions

Odd functions

Odd functions

Reciprocal Identities:

Pythagorean Identities:

a ll s tudents t ake c alculus
All Students Take Calculus.

Quad I

cos(A)>0

sin(A)>0

tan(A)>0

sec(A)>0

csc(A)>0

cot(A)>0

cos(A)<0

sin(A)>0

tan(A)<0

sec(A)<0

csc(A)>0

cot(A)<0

Quad II

cos(A)<0

sin(A)<0

tan(A)>0

sec(A)<0

csc(A)<0

cot(A)>0

cos(A)>0

sin(A)<0

tan(A)<0

sec(A)>0

csc(A)<0

cot(A)<0

Quad IV

Quad III

sine graphs
Sine graphs

y = sin(x)

y = sin(x) + 3

y = 3sin(3x-9)+3

y = sin(x)

y = sin(3x)

y = sin(x/3)

y = sin(x – 3)

y = 3sin(x)

graphs of cosine
Graphs of cosine

y = cos(x)

y = 3cos(x)

y = cos(x) + 3

y = cos(3x)

y = cos(x – 3)

y = 3cos(3x – 9) + 3

y = cos(x)

y = cos(x/3)

graphs of secant and cosecant
Graphs of secant and cosecant

y = sec(x)

y = cos(x)

y = csc(x)

y = sin(x)

law of sines law of cosines
Law of Sines & Law of Cosines

Law of sines

Law of cosines

Use when you haveSSA.

Use when you have SAS, SSS.