The vertical displacement of a specialized laboratory sensor, $V$ , is modelled by the function $V(θ)=8cos⁡θ+15sin⁡θV(\theta) = 8\cos \theta + 15\sin \theta$ , where $θ\theta$ is the phase angle in radians.

Express $V(θ)V(\theta)$ in the form $Rcos⁡(θ−α)R\cos(\theta - \alpha)$ , where $R > 0$ and $\alpha < \frac{\pi}{2}$ . Give the exact value of $R$ and the value of $α\alpha$ , in radians, to 3 decimal places.

A secondary performance metric for the sensor, $H (t)$ , is defined by $H (t) = 12 - 3 V (4 t)$ , for $\ge 0$ , where $t$ is the time in seconds.

Using the answer to part (a), (i) determine the exact maximum value of $H (t)$ . (ii) find the smallest positive value of $t$ for which this maximum value occurs, giving your answer to 2 decimal places.

A secondary performance metric for the sensor, $H (t)$ , is defined by $H (t) = 12 - 3 V (4 t)$ , for $\ge 0$ , where $t$ is the time in seconds.

1.8.6 Compound and double angle formulae (A-level only)

Question 35

Markscheme

1.8.6 Compound and double angle formulae (A-level only)

Question 35

Markscheme

1.8.6 Compound and double angle formulae (A-level only)

Question 35

1.8.6 Compound and double angle formulae (A-level only) Questions

1.8.6 Compound and double angle formulae (A-level only)

Question 35

1.8.6 Compound and double angle formulae (A-level only) Questions