Card 1 of 20
EasyStudy card 1
Prompt
What is \(\sin\theta\) in a right triangle?
Answer
Opposite leg divided by hypotenuse.
MathChapter 15: Trigonometric Functions
Flashcards
Trigonometric Ratios of Acute Angles Flashcards
Twenty concise cards on right-triangle side labels, six ratios, cofunctions, identities, and common traps.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What is \(\cos\theta\) in a right triangle?
Answer
Adjacent leg divided by hypotenuse.
Card 3 of 20
EasyStudy card 3
Prompt
What is \(\tan\theta\) in a right triangle?
Answer
Opposite leg divided by adjacent leg.
Card 4 of 20
EasyStudy card 4
Prompt
Which function is reciprocal to sine?
Answer
Cosecant: \(\csc\theta=1/\sin\theta\).
Card 5 of 20
EasyStudy card 5
Prompt
Which function is reciprocal to cosine?
Answer
Secant: \(\sec\theta=1/\cos\theta\).
Card 6 of 20
EasyStudy card 6
Prompt
Which function is reciprocal to tangent?
Answer
Cotangent: \(\cot\theta=1/\tan\theta\).
Card 7 of 20
EasyStudy card 7
Prompt
Which side is always the hypotenuse?
Answer
The side opposite the right angle.
Card 8 of 20
MediumStudy card 8
Prompt
What changes when the selected acute angle changes?
Answer
The opposite and adjacent leg labels swap; the hypotenuse does not.
Card 9 of 20
MediumStudy card 9
Prompt
What does SOH-CAH-TOA encode?
Answer
Sine=Opposite/Hypotenuse, Cosine=Adjacent/Hypotenuse, Tangent=Opposite/Adjacent.
Card 10 of 20
MediumStudy card 10
Prompt
State the sine-cosine cofunction identity.
Answer
\(\sin\theta=\cos(90^\circ-\theta)\).
Card 11 of 20
MediumStudy card 11
Prompt
State the tangent-cotangent cofunction identity.
Answer
\(\tan\theta=\cot(90^\circ-\theta)\).
Card 12 of 20
MediumStudy card 12
Prompt
State the Pythagorean sine-cosine identity.
Answer
\(\sin^2\theta+\cos^2\theta=1\).
Card 13 of 20
MediumStudy card 13
Prompt
How are tangent, sine, and cosine related?
Answer
\(\tan\theta=\sin\theta/\cos\theta\).
Card 14 of 20
MediumStudy card 14
Prompt
What should you do when one side of a right triangle is missing?
Answer
Use \(a^2+b^2=c^2\) before forming a trig ratio.
Card 15 of 20
MediumStudy card 15
Prompt
If acute \(\theta\) has \(\sin\theta=3/5\), what is \(\cos\theta\)?
Answer
\(4/5\), from a 3-4-5 triangle.
Card 16 of 20
MediumStudy card 16
Prompt
How does an altitude help in an isosceles triangle?
Answer
It bisects the base and creates two congruent right triangles.
Card 17 of 20
HardStudy card 17
Prompt
Why is \(\sin^{-1}x\) not cosecant?
Answer
The superscript \(-1\) denotes inverse sine; cosecant is \(1/\sin x\).
Card 18 of 20
HardStudy card 18
Prompt
If \(\tan\theta=a/b\), what sides can you model?
Answer
Opposite \(a\), adjacent \(b\), and hypotenuse \(\sqrt{a^2+b^2}\).
Card 19 of 20
HardStudy card 19
Prompt
For acute \(\theta\), which root is used in \(\cos\theta=\sqrt{1-\sin^2\theta}\)?
Answer
The positive root, because cosine is positive for an acute angle.
Card 20 of 20
HardStudy card 20
Prompt
What is the safest order for a diagram-based trig problem?
Answer
Select angle → label sides → find missing side → choose ratio → simplify exactly.
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