IB AA SL: core and optional content Core: angle units, rotation, reference angles and signs of sin, cos and tan. Optional: parenthetical cosec, cot and sec sign entries. Measure rotations from the positive $x$-axis: anticlockwise is positive; clockwise is negative. Basic angle The reference angle $\alpha$ is the acute angle to the $x$-axis. The quadrant determines the signs. Degrees and radians $180^\circ=\pi\text{ rad}$ ConversionRuleExample Degrees to radians Radians to degrees $90^\circ=\dfrac\pi2,\quad270^\circ=\dfrac{3\pi}2,\quad360^\circ=2\pi$. Set the calculator to the angle unit used in the question. Signs and quadrants QuadrantPositive thereAngle $\theta$ from basic angle $\alpha$Sketch I II III IV Negative angles and full revolutions SituationRuleExample Negative angle (clockwise turn) Beyond one revolution In the periodic identities, $k\in\mathbb Z$. Measure the basic angle from the $x$-axis.

Basics of Angles

IB AA SL: core and optional content

Core: angle units, rotation, reference angles and signs of sin, cos and tan. Optional: parenthetical cosec, cot and sec sign entries.

Measure rotations from the positive $x$-axis: anticlockwise is positive; clockwise is negative.

Basic angle

The reference angle $\alpha$ is the acute angle to the $x$-axis. The quadrant determines the signs.

Degrees and radians

$180^\circ=\pi\text{ rad}$

Conversion	Rule	Example
Degrees to radians
Radians to degrees

$90^\circ=\dfrac\pi2,\quad270^\circ=\dfrac{3\pi}2,\quad360^\circ=2\pi$.

Set the calculator to the angle unit used in the question.

Signs and quadrants

Quadrant	Positive there	Angle $\theta$ from basic angle $\alpha$	Sketch
I
II
III
IV

Negative angles and full revolutions

Situation	Rule	Example
Negative angle (clockwise turn)
Beyond one revolution

In the periodic identities, $k\in\mathbb Z$. Measure the basic angle from the $x$-axis.

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