3.8 Unit circle and trigonometric identitiesIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

What are the coordinates of the point at angle \theta on the unit circle?
State the Pythagorean identity.
Define \tan\theta using sine and cosine.
At which angles in 0^\circ\le\theta\le360^\circ is \tan\theta undefined?
In which direction and from where is the angle \theta measured on the unit circle?
Which quadrants have \sin\theta0?
Which quadrants have \cos\theta0?
Which coordinate of the point on the unit circle gives the graph of y=\sin\theta?
What are the period and amplitude of y=\cos\theta?
Why can the sine rule give two triangles?
When does the ambiguous case give two triangles?
Period of y=a\sin(bx)+d in degrees?
How do you solve \sin x=0.3 in 0^\circ\le x\le360^\circ with the GDC?

Exam questions on 3.8 Unit circle and trigonometric identities

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).