3.8 Unit circle and trigonometric identitiesIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 3.8 Unit circle and trigonometric identities

1. A point $P$ on the unit circle, centre $O(0,0)$, has coordinates $(x,\,0.6)$ with $x<0$. The angle $\theta$ is measured anticlockwise from the positive $x$-axis to $OP$, where $0^\circ<\theta<180^\circ$.
   Find the size of $\theta$.2 marks
2. A point $Q$ moves anticlockwise round the unit circle, starting at $(1,0)$. After turning through an angle $\theta$ from its start, $Q$ has coordinates $(\cos\theta,\sin\theta)$.
   Given that $\cos\theta=-0.28$ and that $Q$ is below the $x$-axis, find the value of $\sin\theta$.2 marks
3. In triangle $ABC$, $AB=12$ cm, $BC=9$ cm and $B\hat{A}C=40^\circ$.
   Use the sine rule to find the two possible sizes of $A\hat{C}B$.3 marks