IB Mathematics (HL)/Trigonometry
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[edit] Topic 3: Core - Circular Functions and Trigonometry
Circular functions are based upon the unit circle.
[edit] Length of an Arc
Arc Length = r*theta, where r represent the radius of the arc/circle and theta represents the angle in radians between the two lines between the centre of the circle and the arc.
This is merely a derivation from the circumference formula, which equals 2PIr, where 2PI or 360 degrees is the angle.
[edit] Identities
[edit] Pythagorean Identities
sin2x + cos2x = 1
1 + tan2x = sec2x
1 + cot2x = csc2x
[edit] Compound Angle Identities
[edit] Double Angle Identities
[edit] Sine and Cosine Rules and Triangle Areas
[edit] Sine Rule
a/(Sin A) = b/(Sin B) = c/(Sin C) and (Sin A)/a = (Sin B)/b = (Sin C)/c
[edit] Cosine Rule
a2=b2+c2-2bccosA b2=a2+c2-2accosB c2=a2+b2-2abcosC
[edit] Area of a Triangle
½abSinC ½acSinB ½bcSinA
