Trigonometric functions Questionbank

A sinusoidal graph of the form $y = a \cos(b(x - h)) + k$, where $a, b > 0$, has its first maximum point at $(25^\circ, 12)$ and the immediately following point where the graph intersects its midline $y = k$ at $(55^\circ, 7)$. What are the amplitude and the period of this function?

Determine the value of the expression $\sin(90^\circ) - \cos(180^\circ)$.

Find the range of the function $y = -2 \cos(3x) + 1$.

What is the amplitude of the trigonometric function $y = -10 \sin x + 4$?

On a graph of a sinusoidal function, the horizontal distance between a peak (maximum) and the very next trough (minimum) is $90^\circ$. What is the period of this function?

A sinusoidal model is required for a graph that starts at a maximum value when $x = 0$, has an amplitude of $2$, a midline of $y = -1$, and completes exactly $3$ cycles in $360^\circ$. Which equation represents this model?

Consider the sinusoidal function given by the equation $y = a \sin(b(x-h)) + k$, where $a, b, h, k \in \mathbb{R}$. Which of the following correctly describes the amplitude and the equation of the midline of this function?

Determine the phase shift of the function $y = \cos(0.5x + 30^\circ)$ by rewriting it in the standard form $y = a \cos(b(x-h)) + k$.

What is the $y$-coordinate of the function $y = 4 \cos x - 1$ at the point where $x = 180^\circ$?

True or False: Translating the basic sine graph $y = \sin x$ by $90^\circ$ to the right results in the graph of $y = \cos x$.