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India
Class XI

Relative acute angles

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.

a

Find the value of $\alpha$α when $0\le\alpha<2\pi$0α<2π.

b

Find the value of $\alpha$α when $-2\pi<\alpha\le0$2π<α0.

Easy
4min

$A$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.

Easy
3min

$A$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.

Easy
3min

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.

Easy
1min
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Outcomes

11.SF.TF.1

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^2 x + cos^2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: cot(x + or - y), sin x + sin y, cos x + cos y, sin x - sin y, cos x - cos y (see syllabus document)

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