TRIGONOMETRIC MEMORY NOTES (EXACT ROOTS & 2 SIGNIFICANT FIGURES)
ROOT APPROXIMATIONS
$\sqrt{2} \approx 1.41$
$\sqrt;{3} \approx 1.73$
$\sqrt{6} \approx 2.45$
QUADRANT SIGN RULES (ASTC)
Quadrant I (0° to 90°): All functions are positive.
Quadrant II (90° to 180°): Sine is positive ($\sin(180^\circ-\theta) = \sin\theta$).
Quadrant III (180° to 270°): Tangent is positive ($\tan(180^\circ+\theta) = \tan\theta$).
Quadrant IV (270° to 360°): Cosine is positive ($\cos(360^\circ-\theta) = \cos\theta$).
ANGLE: 0°
$\sin 0^\circ = 0 = 0.0$
$\cos 0^\circ = 1 = 1.0$
$\tan 0^\circ = 0 = 0.0$
ANGLE: 15°
$\sin 15^\circ = \dfrac{\sqrt{6}-\sqrt{2}}{4} \approx 0.26$
$\cos 15^\circ = \dfrac{\sqrt{6}+\sqrt{2}}{4} \approx 0.97$
$\tan 15^\circ = 2-\sqrt{3} \approx 0.27$
ANGLE: 30°
$\sin 30^\circ = \dfrac{1}{2} = 0.50$
$\cos 30^\circ = \dfrac{\sqrt{3}}{2} \approx 0.87$
$\tan 30^\circ = \dfrac{\sqrt{3}}{3} \approx 0.58$
ANGLE: 37° (3-4-5 Triangle)
$\sin 37^\circ \approx \dfrac{3}{5} = 0.60$
$\cos 37^\circ \approx \dfrac{4}{5} = 0.80$
$\tan 37^\circ \approx \dfrac{3}{4} = 0.75$
ANGLE: 45°
$\sin 45^\circ = \dfrac{\sqrt{2}}{2} \approx 0.71$
$\cos 45^\circ = \dfrac{\sqrt{2}}{2} \approx 0.71$
$\tan 45^\circ = 1 = 1.0$
ANGLE: 53° (3-4-5 Triangle)
$\sin 53^\circ \approx \dfrac{4}{5} = 0.80$
$\cos 53^\circ \approx \dfrac{3}{5} = 0.60$
$\tan 53^\circ \approx \dfrac{4}{3} \approx 1.3$
ANGLE: 60°
$\sin 60^\circ = \dfrac{\sqrt{3}}{2} \approx 0.87$
$\cos 60^\circ = \dfrac{1}{2} = 0.50$
$\tan 60^\circ = \sqrt{3} \approx 1.7$
ANGLE: 75°
$\sin 75^\circ = \dfrac{\sqrt{6}+\sqrt{2}}{4} \approx 0.97$
$\cos 75^\circ = \dfrac{\sqrt{6}-\sqrt{2}}{4} \approx 0.26$
$\tan 75^\circ = 2+\sqrt{3} \approx 3.7$
ANGLE: 90°
$\sin 90^\circ = 1 = 1.0$
$\cos 90^\circ = 0 = 0.0$
$\tan 90^\circ = \text{Undefined}$
ANGLE: 120°
$\sin 120^\circ = \dfrac{\sqrt{3}}{2} \approx 0.87$
$\cos 120^\circ = -\dfrac{1}{2} = -0.50$
$\tan 120^\circ = -\sqrt{3} \approx -1.7$
ANGLE: 135°
$\sin 135^\circ = \dfrac{\sqrt{2}}{2} \approx 0.71$
$\cos 135^\circ = -\dfrac{\sqrt{2}}{2} \approx -0.71$
$\tan 135^\circ = -1 = -1.0$
ANGLE: 150°
$\sin 150^\circ = \dfrac{1}{2} = 0.50$
$\cos 150^\circ = -\dfrac{\sqrt{3}}{2} \approx -0.87$
$\tan 150^\circ = -\dfrac{\sqrt{3}}{3} \approx -0.58$
ANGLE: 180°
$\sin 180^\circ = 0 = 0.0$
$\cos 180^\circ = -1 = -1.0$
$\tan 180^\circ = 0 = 0.0$
ANGLE: 210°
$\sin 210^\circ = -\dfrac{1}{2} = -0.50$
$\cos 210^\circ = -\dfrac{\sqrt{3}}{2} \approx -0.87$
$\tan 210^\circ = \dfrac{\sqrt{3}}{3} \approx 0.58$
ANGLE: 225°
$\sin 225^\circ = -\dfrac{\sqrt{2}}{2} \approx -0.71$
$\cos 225^\circ = -\dfrac{\sqrt{2}}{2} \approx -0.71$
$\tan 225^\circ = 1 = 1.0$
ANGLE: 240°
$\sin 240^\circ = -\dfrac{\sqrt{3}}{2} \approx -0.87$
$\cos 240^\circ = -\dfrac{1}{2} = -0.50$
$\tan 240^\circ = \sqrt{3} \approx 1.7$
ANGLE: 270°
$\sin 270^\circ = -1 = -1.0$
$\cos 270^\circ = 0 = 0.0$
$\tan 270^\circ = \text{Undefined}$
ANGLE: 300°
$\sin 300^\circ = -\dfrac{\sqrt{3}}{2} \approx -0.87$
$\cos 300^\circ = \dfrac{1}{2} = 0.50$
$\tan 300^\circ = -\sqrt{3} \approx -1.7$
ANGLE: 315°
$\sin 315^\circ = -\dfrac{\sqrt{2}}{2} \approx -0.71$
$\cos 315^\circ = \dfrac{\sqrt{2}}{2} \approx 0.71$
$\tan 315^\circ = -1 = -1.0$
ANGLE: 330°
$\sin 330^\circ = -\dfrac{1}{2} = -0.50$
$\cos 330^\circ = \dfrac{\sqrt{3}}{2} \approx 0.87$
$\tan 330^\circ = -\dfrac{\sqrt{3}}{3} \approx -0.58$
ANGLE: 360°
$\sin 360^\circ = 0 = 0.0$
$\cos 360^\circ = 1 = 1.0$
$\tan 360^\circ = 0 = 0.0$