29 Questions
What determines the vertex of an angle?
The endpoint of the rotating arm
What is the direction of rotation that forms a positive angle 𝜃?
Counter-clockwise direction
What is an angle called if its vertex is at the origin and it originates from the positive 𝒙 − 𝒂𝒙𝒊𝒔?
Standard Position angle
What type of angle is formed when the terminal arm is rotated clockwise about the vertex?
Negative angle
What is the term for the arm that rotates around the vertex?
Terminal arm
What is the range of a reference angle?
0° ≤ 𝜃′ ≤ 90°
What is the formula to find the reference angle for 𝜃 in Quadrant 2?
𝜃′ = 180° − 𝜃
What is the reference angle for a rotation of 200°?
20°
What is the definition of a radian?
An angle of 1 radian, rotated counter-clockwise, of arc length of 1 on a unit circle
What is the unit circle used for?
To measure the arc length of a circle
What is the circumference of a unit circle?
2π
What is the purpose of radians in science and engineering?
To measure the arc length of a circle
What is the relationship between degrees and radians in one full rotation?
360° = 2π
What is the radian measure of 45°?
π/4
What is the degree measure of 5π/6 radians?
225°
What is the simplified form of the radian measure of 315°?
7π/4
What is the degree measure of 2.5 radians?
143°
What is the term for angles in Standard Position that have the same terminal side?
Co-Terminal Angles
What is the result of adding 360° to a given angle?
A co-terminal angle
How do you find the smallest positive co-terminal angle for a given angle?
Divide the given angle by 360 to find the number of full rotations
What is the reference angle for a given angle 𝜽 in Standard Position?
The positive acute angle formed with the terminal side of 𝜽 and the 𝒙-axis
If 𝜃 = 120°, what is one of the negative angles that are co-terminal with 𝜃?
−240°
What is the result of subtracting 2(360°) from a given angle?
A co-terminal angle
What is the radian measure of the angle 𝒔, given that 𝒔 = 4.8 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 and 𝒔 = 24𝑐𝑚?
5.33 𝑟𝑎𝑑𝑖𝑎𝑛𝑠
In which quadrant is the angle 1100°?
Not in a specific quadrant
What is the degree measure of the rotation 1/6 of a full rotation?
30°
What is the radian measure of the angle 90° in terms of 𝜋?
𝜋/2
What is the coterminal angle of 150° in the range [-360°, 0°)?
-450°
What is the radian measure of the angle 630°, expressed to three decimals?
10.995 𝑟𝑎𝑑𝑖𝑎𝑛𝑠
Review the fundamentals of trigonometry, including angles in standard position, vertex, and terminal arm. Understand how angles can rotate in clockwise and counter-clockwise directions.
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