Mathematical Methods — Question 6

QCAA 2025, Paper 2 · 1 mark

Q6 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 6

Solve the equation

\cos(\theta)=-0.6

for

0^\circ\le\theta\le360^\circ

(A)

53.13^\circ

and

126.87^\circ

(B)

53.13^\circ

and

233.13^\circ

(C)

126.87^\circ

and

306.87^\circ

(D)

126.87^\circ

and

233.13^\circ

ABCD

WORKED SOLUTION

1 mark

ANSWER

D —

126.87^\circ

and

233.13^\circ

Worked solution

The reference angle is

\cos^{-1}(0.6)=53.13^\circ

. Cosine is negative in quadrants II and III, giving

180^\circ-53.13^\circ=126.87^\circ

and

180^\circ+53.13^\circ=233.13^\circ

; option D.

Selects option D.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.