Purpose: Self-check your understanding. This quiz is not graded.
Click "Check Answer" for instant feedback and "Show Solution" for detailed explanations with rendered formulas.
Score: 0 / 3
5.2 — Transformations of Sinusoidal Functions
Question 1
For \( y = 3\sin\left(2\left(x - \frac{\pi}{4}\right)\right) + 1 \), the amplitude is:
Solution:
In \( y = a\sin(k(x-d))+c \), the amplitude is \( |a| = |3| = 3 \).
Question 2
The period of \( y = 3\sin\left(2\left(x - \frac{\pi}{4}\right)\right) + 1 \) is:
Solution:
Period \( = \frac{2\pi}{|k|} = \frac{2\pi}{2} = \pi \).
5.4 — Solving Trig Equations
Question 3
How many solutions does \( 2\sin(x) - 1 = 0 \) have on \( [0, 2\pi) \)?
Solution:
\( \sin(x) = \frac{1}{2} \). On \( [0, 2\pi) \), sine equals \( \frac{1}{2} \) at \( x = \frac{\pi}{6} \) (Q1) and \( x = \frac{5\pi}{6} \) (Q2). Two solutions.