2.2.11 Trigonometric Values

Trigonometry problems have been increasingly popular for writers of the number sense test.

Special Angles (Quadrant I)

Function	0°	30°	45°	60°	90°
sin	0	1/2	$\sqrt{2}/2$	$\sqrt{3}/2$	1
cos	1	$\sqrt{3}/2$	$\sqrt{2}/2$	1/2	0
tan	0	$\sqrt{3}/3$	1	$\sqrt{3}$	Undef
csc	Undef	2	$\sqrt{2}$	$2\sqrt{3}/3$	1
sec	1	$2\sqrt{3}/3$	$\sqrt{2}$	2	Undef
cot	Undef	$\sqrt{3}$	1	$\sqrt{3}/3$	0

Signs in Quadrants (ASTC)

• Quadrant I (All): All positive
• Quadrant II (Students): Sin/Csc positive
• Quadrant III (Take): Tan/Cot positive
• Quadrant IV (Calculus): Cos/Sec positive

Reference Angles

Quadrant	Reference Angle Formula
I	$\theta$
II	$180^\circ - \theta$
III	$\theta - 180^\circ$
IV	$360^\circ - \theta$

Example: $\sin(210^\circ)$ Q-III (sin is negative). Ref angle = $210^\circ - 180^\circ = 30^\circ$. $\sin(210^\circ) = -\sin(30^\circ) = -1/2$.

Problem Set 2.2.11