Interactive practice questions
A line through two points on the unit circle, $A$A and $B$B, also passes through the origin, $O$O. The line segment $OB$OB forms an angle of $\theta=\frac{\pi}{13}$θ=π13 with the positive $x$x-axis. This is shown in the diagram below.
The angle between the line segment $OA$OA and the positive $x$x-axis is $\alpha$α.
Find the value of $\alpha$α when $0\le\alpha<2\pi$0≤α<2π.
Find the value of $\alpha$α when $-2\pi<\alpha\le0$−2π<α≤0.
$A$A and $B$B are two points on the unit circle centred at the origin, $O$O. The line segment $OA$OA forms an angle of $\theta=\frac{\pi}{7}$θ=π7 with the positive $x$x-axis, and the line passing through $A$A and $B$B is parallel to the $x$x-axis. This is shown in the diagram below.
The angle between the line segment $OB$OB and the positive $x$x-axis is $\alpha$α.
$A$A and $B$B are two points on the unit circle centred at the origin, $O$O. The line segment $OA$OA forms an angle of $\theta=\frac{\pi}{11}$θ=π11 with the positive $x$x-axis, and the line passing through $A$A and $B$B is parallel to the $y$y-axis. This is shown in the diagram below.
The angle between the line segment $OB$OB and the positive $x$x-axis is $\alpha$α.
Consider the unit circle below, where the line through $A$A and $B$B is parallel to the $x$x-axis.
Suppose that $\theta=\frac{10\pi}{11}$θ=10π11. State the value of the reference angle, $\alpha$α.