Exact trigonometric values and symmetry

Practise exact trigonometric values and symmetry with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $f(x)=2\sin x-\cos x$. (a) Find $f(\pi/6)$ exactly. [2 marks] (b) Find $f(5\pi/6)$ and hence their sum. [2 marks]

Worked explanation

• Part (a)

  Use $\sin(\pi/6)=1/2$ and $\cos(\pi/6)=\sqrt3/2$, giving $f(\pi/6)=1-\sqrt3/2$.

• Part (b)

  In quadrant II, sine is $1/2$ and cosine is $-\sqrt3/2$. Thus the second value is $1+\sqrt3/2$ and the radical terms cancel in the sum.

(a) $1-\sqrt3/2$.; (b) $1+\sqrt3/2$; sum $2$.

Original VectorPaths practice; not an official VCAA question or marking rubric.