3.35: Factorised sine–cosine equation and a secant equation

0606/11/M/J/21 — Question 9 · 10 marks

(a)(i)

Write

6xy + 3x + 4y + 2

in the form

(ax + b)(cy + d)

, where

a

,

b

,

c

and

d

are positive integers.

[1]

(a)(ii)

Hence solve

6\sin\theta\cos\theta + 3\sin\theta + 4\cos\theta + 2 = 0

for

0\degree \leqslant \theta \leqslant 360\degree

.

[4]

(b)

Solve

\sec\!\left(z + \dfrac{\pi}{4}\right) = 2

for

-\pi \leqslant z \leqslant \pi

, where

z

is in radians. Give your answers in terms of

\pi

.

[5]