3.5 Trigonometry (A-level only)

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Question 90

Express $3cos⁡x+2sin⁡x3\cos x + 2\sin x$ in the form $Rcos⁡(x−α)R\cos(x - \alpha)$ , 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.

[4]

A researcher is monitoring the depth of water in a tidal harbor. The depth of the water, $D$ meters, is modeled by the equation

\frac{15}{4 + 3\cos(0.4t) + 2\sin(0.4t)}, \quad 0 \le t \le 12

where $t$ is the number of hours after midnight.

Find, according to the model: the minimum depth of the water in the harbor, giving your answer to 2 decimal places,

[3]

the value of $t$ , to 2 decimal places, when $D = 3.5$ .

[4]

3.5 Trigonometry (A-level only)

Question 90

[4]

A researcher is monitoring the depth of water in a tidal harbor. The depth of the water, $D$ meters, is modeled by the equation

\frac{15}{4 + 3\cos(0.4t) + 2\sin(0.4t)}, \quad 0 \le t \le 12

where $t$ is the number of hours after midnight.

Find, according to the model: the minimum depth of the water in the harbor, giving your answer to 2 decimal places,

[3]

the value of $t$ , to 2 decimal places, when $D = 3.5$ .

[4]

3.5 Trigonometry (A-level only)

Question 90

Markscheme

3.5 Trigonometry (A-level only)

Question 90

Markscheme

3.5 Trigonometry (A-level only)

Question 90

3.5 Trigonometry (A-level only) Questions

3.5 Trigonometry (A-level only)

Question 90

3.5 Trigonometry (A-level only) Questions