Worksheets · Foundation and Higher

Exact trigonometric values

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 3 marks

   Write down the exact value of each expression.

   (a) $\sin 30^\circ$ (1)

   (b) $\cos 60^\circ$ (1)

   (c) $\tan 45^\circ$ (1)
2. Question 2Non-calculator · 4 marks

   In triangle PQR, angle Q = $90^\circ$, angle P = $60^\circ$ and PQ = 5 cm.

   (a) Find the exact length of PR. (2)

   (b) Find the exact length of QR. (2)
3. Question 3Non-calculator · 6 marks

   In triangle $ABC$, $D$ is the point on $BC$ such that $AD$ is perpendicular to $BC$. $AD = 6$ cm, angle $ABD = 30^\circ$ and angle $ACD = 45^\circ$.

   (a) Work out the exact length of $BC$. Give your answer in the form $a + b\sqrt{3}$. (4)

   (b) Work out the exact length of $AB$. (2)