precal unit 4- intro to trigonometry

what is a radius length arc called?

a radian

a one radian angle intercepts an arc of _________ length

one radius

trigonometry

greek word for the measurement of triangles

central angle of a circle

angle with the vertex at the center of a circle

degree

a rotation of 1/360 of a complete revolution around a circle

a angle is determined by...

rotating a ray about its endpoint

the initial side of an angle is...

starting position of the ray

the terminal side of an angle is...

the position of the ray after rotation

the vertex of an angle is...

end point of ray

an angle is in standard position when...

the vertex is at the original of a coordinate plane and the initial side coincides with the positive x-axis

a positive angle is generated by a ____________ rotation

counterclockwise

if two angles are coterminal then they have...

the same initial and terminal sides

the measure of an angle is determined by...

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

One radian is the measure of a central angle theta that

intercepts an arc S equal in length to the radius of the circle

angles with measures between pi and pi/2 are...

acute

angles with measures between pi/2 and 2pi are...

obtuse

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

add/subtract 2pi

to convert degrees to radians...

multiply by π/180

to convert radian to degrees

multiply by 180/pi

arc length equation

s=rθ

if r=1, then S= ____ and the radian measure of theta equals ______

theta, arc length

linear speed equation

v=s/t (arc length/time)

linear speed

a particle moving at constant speed along a circular arc of radius r, how fast the particle moves

angular speed equation

w=θ/t

angular speed

how fast the angle changes

a sector of a circle is...

the region bounded by two radii of the circle and their intercepted arc

area of a sector

A=1/2r^2θ

cosecant is the inverse of...

sine

secant is the inverse of...

cosine

quotient identities. tan theta=

sin theta/cos theta

quotient identities. cot theta=

cos theta/sin theta

Pythagorean identities

sin^2(θ)+cos^2(θ)=1
1+tan^2(θ)=sec^2(θ)
1+cot^2(θ)=csc^2(θ)

side length of a 45-45-90 triangle

x, x, x√2

Side Lengths of a 30-60-90 Triangle

x, x√3, 2x

to 'solve a right triangle' means...

find all the missing measure of a right triangle

angle of elevation

angle formed with the horizontal upward to an object, always inside the triangle

angle of depression

angle formed w the horizontal downward to an object, always outside the triangle

a unit circle is a circle with a radius of....

1

which functions are positive in quadrant 1?

all

which functions are positive in quadrant 2?

sin & csc

which functions are positive in quadrant 3?

tan & cot

which functions are positive in quadrant 4?

cos & sec

reference angles

the acute angle formed by the terminal side and the horizontal axis, always positive

Sine is an ______ function

odd

if you do sine of a positive number, and then its negative equivalent, what would happen to your solution?

it would switch to negative

if you do cosine of a positive number, and then its negative equivalent, what would happen to your solution?

it would remain the same

cosine is an _____ function

even