Pre-Cal Quiz 1 Q2 Flashcards
An ______ is a plane figure consisting of two rays having the same endpoint.
angle
The sides of an angle are the _____; one is the _____ side, the other is the ________ side.
rays; initial and terminal
A ________ of a circle is an angle whose sides’ common endpoint, its vertex, is at the center of the circle.
central angle
An _______ is formed by rotating a ray about its endpoint.
angle
An angle is positive if the ray rotates in a a. __________ direction, and the angle is negative if it rotates in a b. __________ direction.
a. counterclockwise
b. clockwise
If an angle fits a coordinate system in which the origin is the vertex and the initial side coincides with the positive x-axis, then this angle is said to be an ______________________.
Angle in Standard Position
A central angle of a circle measures __________ if it intercepts 1/360 of the circumference of the circle.
one degree (1°)
a. __________ is 1/60 of 1°
b. __________ is 1/60 of 1’
a. One minute (1’)
b. One second (1’’)
The unit circle is the circle given by the equation a. _____________ where the center is b. ___________ and radius of c. ___
a. x^2 + y^2 = 1
b. at the origin
c. 1
A central angle of the unit circle that intercepts an arc s of the circle with length 1 unit is said to have a measure of __________.
One radian (1 rad)
Circumference of a circle is ________.
2πr
The radian measure of an angle of ONE FULL REVOLUTION in a unit circle is ______.
2π
a. To convert degree to radian. Multiply by _______.
b. To convert radian to degree. Multiply by _______.
a. π/180
b. 180/π
In a circle, a central angle whose radian measure is θ subtends an arc that is the fraction _______ of the circumference of the circle.
θ/2π
a. What is the symbol for arc length?
b. What is the formula for arc lenght?
a. s
b. rθ
A ________ of a circle is the portion of the interior of a circle bounded by the initial and terminal sides of a central angle and intercepted arc.
sector
a. What is the symbol for sector area?
b. What is its formula?
a. A (ALWAYS REMEMBER THAT THE ANSWER’S MEASUREMENT IS SQUARED)
b. 1/2θr^2
Two angles in standard position that have a common terminal side are called ______________.
Coterminal Angles
The measure of coterminal angles differ by __________________.
multiples of 360° or 2π
If s is a real number and P(x, y) is the point on the unit circle U that corresponds to s, then:
sin s = y, cos s = x, tan s = y/x
The formulas in this definition express function values in terms of coordinates of a point P on a unit circle. For this reason, the trigonometric functions are sometimes referred to as the ________________.
circular functions
The signs of each circular function in each quadrant:
QI - all functions are positive since x & y are positive.
QII - sin and csc are positive since y is positive.
QIII - tan and cot are positive since x & y are negative
QIV - cos and sec are positive since x is positive
The reference angle for θ is the acute angle denoted by θR. It is the angle between the ___________________.
terminal side and x-axis
Formulas to find degree and radian measure of θR.
QI: θR = θ
QII: θR = 180° - θ; θR = π - θ
QIII: θR = θ - 180°; θ - π
QIV: θR = 360° - θ ; θR = 2π - θ
