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Trigonometric Functions · Paper 2 — Free Maths AI SL Practice Questions

1MasterySAQ-STrigonometric identities and equations6 marksPaper 2~9 min

A particle moves along a straight line. Its displacement

s

(in metres) from a fixed point at time

t

(in seconds) is given by

s(t) = 3\sin(2t) - 4\cos(2t)

(a)

Show that

s(t)

can be written in the form

R\sin(2t - \alpha)

, where

R > 0

and

0 < \alpha < \dfrac{\pi}{2}

, and determine the values of

R

and

\alpha

. Give

\alpha

correct to three significant figures. [3 marks]

(b)

State the maximum displacement of the particle from the fixed point. [1 mark]

(c)

Calculate the smallest positive value of

t

for which

s(t) = 2

. Give your answer correct to three decimal places. [2 marks]

Solutions

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