You're viewing 1 free preview question for Maths AA HL — subscribe to unlock 11 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Trigonometric Functions · Paper 3 — Free Maths AA HL Practice Questions

1ChallengeLAQSine, cosine, and tangent functionss10 marksPaper 3~15 min

The function

f

is defined by

f(x) = \sin x + \cos x

, for

x \in \mathbb{R}

(a)

Prove that

f(x)

can be written in the form

R\sin(x+\alpha)

, where

R > 0

and

\alpha \in \left[0,\dfrac{\pi}{2}\right]

, stating the exact values of

R

and

\alpha

. [4 marks]

(b)

Hence prove that the equation

f(x) = \dfrac{3}{2}

has no solutions. [3 marks]

(c)

Using your result from (a), determine the number of solutions of the equation

f(x) = k

in the interval

0 \leq x \leq 2\pi

for each possible value of the constant

k \in \mathbb{R}

. Justify your answer. [3 marks]

Solutions

Questions 2-12

Unlock these questions with Premium

That's every free question here — 1 of 12.

+11 more questions, plus Mock Papers & Worksheets, are waiting in Premium.