Page 32 - Ebook Trigonometri_Krisna Hasugian_MESP 2019
P. 32
Double and Half Angle Formulas
Below you will learn formulas that allow you to use the relationship between the
six trig functions for a particular angle and find the trig values of an angle that is
either half or double the original angle.
Double Angle Formulas
cos 2 = cos² − sin² =2cos² − 1 = 1 − 2sin²
sin 2 = 2 sin cos
2 tan
tan 2 =
1 − tan²
Half Angle Formulas
cos = ±√ 1+cos
2 2
1−cos
sin = ±√
2 2
1−cos sin 1−cos
tan = ±√ tan = tan =
2 1+cos 2 1+cos 2 sin
Lets see these formulas in action!
Example 32 Use the double angle formula to find the exact value of each
expression
sin 120°
√3
sin 120° = sin 2(60°) = 2 sin 60° ⋅ cos 60° =
2
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