Trig graphs & transformations
Practice Flashcards
Range of y = sin x and y = cos x?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All Flashcards in Topic 3.7
Below are all 17 flashcards for this topic. Sign up free to track your progress and get personalized review schedules.
3.7.18 cards
Range of y = sin x and y = cos x?
−1 ≤ y ≤ 1.
Period of sin and cos?
360° (2π radians).
Period of tan?
180° (π radians).
Why does tan have asymptotes?
tan = sin/cos, so it blows up where cos x = 0 (90°, 270°, …).
Does tan have an amplitude?
No — it's unbounded (range all reals), so amplitude doesn't apply.
How do you find amplitude from a graph?
Amplitude = (max − min)/2.
How are sin and cos related?
cos x = sin(x + 90°) — same wave shifted left 90°.
Where is the max of y = cos x on 0°–360°?
At x = 0° and x = 360° (cos starts at its max).
3.7.29 cards
In y = a sin(bx) + d, what is a?
The amplitude (vertical stretch).
In y = a sin(bx), what is the period?
360°/b (or 2π/b) — b divides the period.
In y = a sin(bx) + d, what does d do?
Shifts the wave vertically; the midline is y = d.
In y = a sin(b(x − c)) + d, what is c?
The horizontal (phase) shift — right by c.
Amplitude from max and min?
a = (max − min)/2.
Midline (d) from max and min?
d = (max + min)/2.
How do you find b from a period?
b = 2π/period (or 360°/period).
Period of y = 3 sin(2x)?
360°/2 = 180° (or 2π/2 = π).
Check using a and d?
max = d + a, min = d − a.
Topic 3.7 study notes
Full notes & explanations for Trig graphs & transformations
Math AA SL exam skills
Paper structures, command terms & tips
Want smart review reminders?
Sign up free to track your progress. Our spaced repetition algorithm will tell you exactly which cards to review and when.
Start Free