Card 1 of 20
EasyStudy card 1
Prompt
For point \(P(x,y)\), how is \(r\) found?
Answer
\(r=\sqrt{x^2+y^2}\).
MathChapter 15: Trigonometric Functions
Flashcards
Trigonometric Functions of General Angles and the Unit Circle Flashcards
Twenty concise cards on coordinate definitions, exact values, quadrants, reference angles, and axis cases.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
For a general terminal point, what is sine?
Answer
\(\sin\theta=y/r\).
Card 3 of 20
EasyStudy card 3
Prompt
For a general terminal point, what is cosine?
Answer
\(\cos\theta=x/r\).
Card 4 of 20
EasyStudy card 4
Prompt
For a general terminal point, what is tangent?
Answer
\(\tan\theta=y/x\), provided \(x\ne0\).
Card 5 of 20
EasyStudy card 5
Prompt
What equation defines the unit circle?
Answer
\(x^2+y^2=1\).
Card 6 of 20
EasyStudy card 6
Prompt
What is the unit-circle point for angle \(\theta\)?
Answer
\((\cos\theta,\sin\theta)\).
Card 7 of 20
EasyStudy card 7
Prompt
What side ratio defines a 30-60-90 triangle?
Answer
Short leg : long leg : hypotenuse = \(1:\sqrt3:2\).
Card 8 of 20
MediumStudy card 8
Prompt
What side ratio defines a 45-45-90 triangle?
Answer
Leg : leg : hypotenuse = \(1:1:\sqrt2\).
Card 9 of 20
MediumStudy card 9
Prompt
What are \(\sin30^\circ\) and \(\cos30^\circ\)?
Answer
\(1/2\) and \(\sqrt3/2\), respectively.
Card 10 of 20
MediumStudy card 10
Prompt
What are \(\sin45^\circ\) and \(\cos45^\circ\)?
Answer
Both are \(\sqrt2/2\).
Card 11 of 20
MediumStudy card 11
Prompt
What are \(\sin60^\circ\) and \(\cos60^\circ\)?
Answer
\(\sqrt3/2\) and \(1/2\), respectively.
Card 12 of 20
MediumStudy card 12
Prompt
How is a reference angle defined?
Answer
The acute angle between the terminal side and the \(x\)-axis.
Card 13 of 20
MediumStudy card 13
Prompt
Which trig functions are positive in quadrant II?
Answer
Sine and cosecant; cosine, secant, tangent, and cotangent are negative.
Card 14 of 20
MediumStudy card 14
Prompt
Which trig functions are positive in quadrant III?
Answer
Tangent and cotangent; sine and cosine families are negative.
Card 15 of 20
MediumStudy card 15
Prompt
Which trig functions are positive in quadrant IV?
Answer
Cosine and secant; sine and tangent families are negative.
Card 16 of 20
MediumStudy card 16
Prompt
When is tangent undefined on the unit circle?
Answer
When \(x=\cos\theta=0\), at \(\pi/2+\pi k\).
Card 17 of 20
HardStudy card 17
Prompt
If \(P=(-8,15)\), what are sine and cosine?
Answer
Since \(r=17\), \(\sin\theta=15/17\) and \(\cos\theta=-8/17\).
Card 18 of 20
HardStudy card 18
Prompt
What is the reference angle for \(220^\circ\)?
Answer
\(40^\circ\), because \(220^\circ-180^\circ=40^\circ\).
Card 19 of 20
HardStudy card 19
Prompt
Why is \(\tan90^\circ\) undefined rather than zero?
Answer
The point is \((0,1)\), so \(y/x=1/0\), which is undefined.
Card 20 of 20
HardStudy card 20
Prompt
What four-step method evaluates a non-axis familiar angle?
Answer
Find quadrant → reference angle → exact magnitude → coordinate-based sign.
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