Trigonometry Vocab

For the negative angle -120°, add 360° to obtain a coterminal angle

-120° + 360° = 240°

CALCULATOR!!!!!!!!!!!!!! Change degrees to degrees, minutes, and seconds.

1. Type in the degrees 2. Press 2nd, Angle, DMS, Enter 3. Round of the seconds because there are NO. DECIMALS!

supplement of an angle

in degrees: 180° - angle in radians: π - angle

complement of an angle

in degrees: 90° - angle in radians: π/2 - angle

s

is the arc length

θ

is the central angle in radians

r

is the radius of the circle

a sector of a circle

is the region bounded by two radii of the cricle and their intercepted arc.

the ratio s/r has no units

it is simply a real number

one degree (1°)

a rotation of 1/360 of a complete revolution about the vertex

radians

a type of measure especially useful in calculus

To find an angle that is coterminal to a given angle θ

add or subtract 360° (one revolution)

coterminal angles

angle + (n)360° where n is an integer

coterminal angles

angles that have the same initial and terminal sides angles that start and stop in the same place but have a different measure

one full revolution

arc length of s = 2πr 2π is about 6.28 just over six radian lengths

Angles are labeled with Greek letters α (alpha), β (beta), and θ (theta)

as well as uppercase A, B, and C

acute angles

between 0° and 90°

obtuse angles

between 90° and 180°

negative angles

clockwise rotation

Two positive angles α and β are

complementary (complements of each other) if their sum is 90°.

positive angles

counterclockwise rotation

angle

determined by rotating a ray (half-line) about its endpoint

Quadrant I

Positive Degrees: 0° < θ < 90° Negative Degrees: -270° < θ < -360° Positive Radians: 0 < radian < π/2 Negative Radians: -3π/2 < radian < 2π

Quadrant III

Positive Degrees: 180° < θ < 270° Negative Degrees: -90° < θ < -180° Positive Radians: π < radian < 3π/2 Negative Radians: -π/2 < radian < -π

Quadrant IV

Positive Degrees: 270° < θ < 360° Negative Degrees: 0° < θ < -90° Positive Radians: 3π/2 < radian < 2π Negative Radians: 0 < radian < -π/2

Quadrant II

Positive Degrees: 90° < θ < 180° Negative Degrees: -180° < θ < -270° Positive Radians: π/2 < radian < π Negative Radians: -π < radian < -3π/2

To convert radians to degrees

Radians x 180°/π

CALCULATOR!!!!!!!!!!!!!! Change degrees, minutes, and seconds to degrees.

1. Type the degree 2. Press 2nd, Angle, and the ° symbol, which is 1 3. Type the minute 4. Press 2nd, Angle, and the ' symbol which is 2 5. Type the seconds 6. Press Alpha, the + button, and then Enter

Solving Right Triangles

1. given on side of a right triangle and one of the acute triangles, find one of the other sides OR 2. given two sides; find one of the acute angles OR 3. find all of the remaining parts

For the positive angle 135°, subtract 360° to obtain a coterminal angle.

135° - 360° = -225°

half revolution (counterclockwise)

180°

1 radian

180°/π

circumference

2πr units

1 revolution

360°

2πr

360°

2πradians

360°

circumference

360°

full revolution (counterclockwise)

360°

For the positive angle 360° subtract 360° to subtract 360° to obtain a coterminal angle.

390° - 360° = 30°

quarter revolution (counterclockwise)

90°

area of a sector of a circle

A = 1/2r^2θ r is the radius of the circle. θ is the central angle IN RADIANS

To convert degrees to radians

Degrees x π/180°

A given angle θ has infinitely many coterminal angles

Example: θ = 30° is coterminal with 30° + n(360°) where n is an integer

trigonometry

Greek for "measurement of triangles"

Angles between 0° and 360°

lie in each of the quadrants

definition of radian

one radian is the measure of a central angle θ that intercepts an arc s equal in length of the radius r of the circle

terminal side

position after rotation

arc length

s = rθ

To evaluate function with a calculator

set the calculator to the desired mode of measurement (degree or radian)

RECIPROCALS

sine (sin) <--> cosecant (csc) cosine (cos) <--> secant (sec) tangent (tan) <--> cotangent (cot)

COFUNCTIONS

sine <--> cosine tangent <--> cotangent secant <--> cosecant

Two positive angles α and β are

supplementary (supplements of each other) if their sum is 180°.

measure of an angle

the amount of rotation from the initial side to the terminal side

standard position of an angle

the angle fits in the coordinate system the initial side coincides with the positive x-axis the vertex is at origin

angle of depression

the angle from the horizontal downward to an object

angle of elevation

the angle from the horizontal upward to an object

vertex

the endpoint of the ray

degrees

the most common unit of angle measure (denoted by the symbol, °)

initial side

the starting position of the ray

If 0° < θ < 90° (θ lies in the first quadrant)

then the value of each trigonometric function is POSITIVE

The reciprocal identities for sine, cosine, and tangent can be used

to evaluate the cosecant, secant, and cotangent functions with a calculator

To measure angles, it is convenient

to mark degrees on the circumference of a circle

To evaluate csc(π/8)

use the reciprocal function: csc(π/8) = 1/sin(π/8)

To evaluate cotangent, secan, and co

use the x^-1 wither their respective reciprocal functions sine, cosine, and tangent.

central angle

vertex is the center of the circle

arc length = radius

when θ = 1 radian

Algebraically, θ - s/r

where θ is measured in radians. (Note: θ = 1 when s = r)

1°

π/180°