A wave travels along a string, and its position in millimeters is described by h ( t ) = 15 ( 2 cos ⁡ t + 1 ) h\left(t\right)=15\left(2\cos t+1\right) , for t ≥ 0 t\geq0 , where t t represents time in seconds. Determine the velocity of the wave, v ( t ) = h ′ ( t ) v\left(t\right)=h^{\prime}\left(t\right) .

v ( t ) = − 30 sin ⁡ t mm/s v\left(t\right)=-30\sin t\text{ mm/s}

v ( t ) = 30 sin ⁡ t mm/s v\left(t\right)=30\sin t\text{ mm/s}

v ( t ) = 15 sec ⁡ 2 t mm/s v\left(t\right)=15\sec^2t\text{ mm/s}

v ( t ) = − 30 csc ⁡ 2 t mm/s v\left(t\right)=-30\csc^2t\text{ mm/s}

Derivatives of Trig Functions

3. Techniques of Differentiation / Derivatives of Trig Functions / Problem 2

Problem 2

A wave travels along a string, and its position in millimeters is described by $h (t) = 15 (2 \cos t + 1)$ , for $t is greater than or equal to 0$ , where $t$ represents time in seconds. Determine the velocity of the wave, $v (t) = h^{'} (t)$ .

$v of t equals 30 sine t mm slash s$

$v (t) = - 30 \sin t mm/s$

$v of t equals 15 secant squared t mm slash s$

$v (t) = - 30 \csc^{2} t mm/s$