Pre-Cal Quiz 1 Q2

Question 1

An ______ is a plane figure consisting of two rays having the same endpoint.

Answer 1

angle

Question 2

The sides of an angle are the _____; one is the _____ side, the other is the ________ side.

Answer 2

rays; initial and terminal

Question 3

A ________ of a circle is an angle whose sides’ common endpoint, its vertex, is at the center of the circle.

Answer 3

central angle

Question 4

An _______ is formed by rotating a ray about its endpoint.

Answer 4

angle

Question 5

An angle is positive if the ray rotates in a a. __________ direction, and the angle is negative if it rotates in a b. __________ direction.

Answer 5

a. counterclockwise
b. clockwise

Question 6

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 ______________________.

Answer 6

Angle in Standard Position

Question 7

A central angle of a circle measures __________ if it intercepts 1/360 of the circumference of the circle.

Answer 7

one degree (1°)

Question 8

a. __________ is 1/60 of 1°
b. __________ is 1/60 of 1’

Answer 8

a. One minute (1’)
b. One second (1’’)

Question 9

The unit circle is the circle given by the equation a. _____________ where the center is b. ___________ and radius of c. ___

Answer 9

a. x^2 + y^2 = 1
b. at the origin
c. 1

Question 10

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 __________.

Answer 10

One radian (1 rad)

Question 11

Circumference of a circle is ________.

Answer 11

2πr

Question 12

The radian measure of an angle of ONE FULL REVOLUTION in a unit circle is ______.

Answer 12

2π

Question 13

a. To convert degree to radian. Multiply by _______.
b. To convert radian to degree. Multiply by _______.

Answer 13

a. π/180
b. 180/π

Question 14

In a circle, a central angle whose radian measure is θ subtends an arc that is the fraction _______ of the circumference of the circle.

Answer 14

θ/2π

Question 15

a. What is the symbol for arc length?
b. What is the formula for arc lenght?

Answer 15

a. s
b. rθ

Question 16

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.

Answer 16

sector

Question 17

a. What is the symbol for sector area?
b. What is its formula?

Answer 17

a. A (ALWAYS REMEMBER THAT THE ANSWER’S MEASUREMENT IS SQUARED)
b. 1/2θr^2

Question 18

Two angles in standard position that have a common terminal side are called ______________.

Answer 18

Coterminal Angles

Question 19

The measure of coterminal angles differ by __________________.

Answer 19

multiples of 360° or 2π

Question 20

If s is a real number and P(x, y) is the point on the unit circle U that corresponds to s, then:

Answer 20

sin s = y, cos s = x, tan s = y/x

Question 21

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 ________________.

Answer 21

circular functions

Question 22

The signs of each circular function in each quadrant:

Answer 22

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

Question 23

The reference angle for θ is the acute angle denoted by θR. It is the angle between the ___________________.

Answer 23

terminal side and x-axis

Question 24

Formulas to find degree and radian measure of θR.

Answer 24

QI: θR = θ
QII: θR = 180° - θ; θR = π - θ
QIII: θR = θ - 180°; θ - π
QIV: θR = 360° - θ ; θR = 2π - θ