Card 1 of 20
EasyStudy card 1
Prompt
What central angle is one radian?
Answer
An angle intercepting an arc whose length equals the circle radius.
MathChapter 15: Trigonometric Functions
Flashcards
The Radian Measure of an Angle Flashcards
Twenty concise cards on radian meaning, exact conversion, standard position, coterminal angles, and periods.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
How many radians are in a full turn?
Answer
\(2\pi\) radians.
Card 3 of 20
EasyStudy card 3
Prompt
Complete the benchmark: \(180^\circ=\ ?\)
Answer
\(\pi\) radians.
Card 4 of 20
EasyStudy card 4
Prompt
Approximately how many degrees is one radian?
Answer
About \(57.3^\circ\).
Card 5 of 20
EasyStudy card 5
Prompt
What factor converts degrees to radians?
Answer
Multiply by \(\pi/180^\circ\).
Card 6 of 20
EasyStudy card 6
Prompt
What factor converts radians to degrees?
Answer
Multiply by \(180^\circ/\pi\).
Card 7 of 20
EasyStudy card 7
Prompt
What is \(90^\circ\) in radians?
Answer
\(\pi/2\).
Card 8 of 20
MediumStudy card 8
Prompt
What is an angle in standard position?
Answer
Its vertex is at the origin and its initial side lies on the positive \(x\)-axis.
Card 9 of 20
MediumStudy card 9
Prompt
Which rotation direction is positive?
Answer
Counterclockwise.
Card 10 of 20
MediumStudy card 10
Prompt
Which rotation direction is negative?
Answer
Clockwise.
Card 11 of 20
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Prompt
What are coterminal angles?
Answer
Angles with the same initial and terminal sides.
Card 12 of 20
MediumStudy card 12
Prompt
How do you generate degree-measure coterminal angles?
Answer
\(\theta+360^\circ k\), where \(k\) is any integer.
Card 13 of 20
MediumStudy card 13
Prompt
How do you generate radian-measure coterminal angles?
Answer
\(\theta+2\pi k\), where \(k\) is any integer.
Card 14 of 20
MediumStudy card 14
Prompt
What is the period of sine and cosine?
Answer
\(360^\circ\), or \(2\pi\) radians.
Card 15 of 20
MediumStudy card 15
Prompt
What is the period of tangent?
Answer
\(180^\circ\), or \(\pi\) radians.
Card 16 of 20
MediumStudy card 16
Prompt
What is \(225^\circ\) in radians?
Answer
\(5\pi/4\).
Card 17 of 20
HardStudy card 17
Prompt
Why can tangent use a half-turn period?
Answer
After \(\pi\), sine and cosine both change sign, leaving their quotient unchanged.
Card 18 of 20
HardStudy card 18
Prompt
Find the least positive angle coterminal with \(-75^\circ\).
Answer
\(285^\circ\).
Card 19 of 20
HardStudy card 19
Prompt
Reduce \(17\pi/6\) to \([0,2\pi)\).
Answer
\(5\pi/6\).
Card 20 of 20
HardStudy card 20
Prompt
What unit-check prevents conversion errors?
Answer
Choose a factor that cancels the given unit and leaves the requested unit.
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