Question

Usando as fórmulas de adição, determine:


a) tg15°

b) sen15°

c) cos75°

d) sen75°

e) sen105°

f) cos195°

Answer 1

a) tg15° = tg (45° - 30°) = 1 - $\sqrt{3}$

b) sen15° = sen (45 - 30) = √2 / 2 - 1/2 = $\frac{\sqrt{2} - 1}{2}$

c) cos 75° = cos (45 + 30) = √2 / 2 + √3 / 2 = $\frac{\sqrt{3} + \sqrt{2}}{2}$

d) sen75° = sen (45 + 30) = √2 / 2 + 1/2 = $\frac{\sqrt{2} + 1}{2}$

e) sen105° = sen (90 + 45 - 30) = 1 + √2 / 2 - 1/2 = $\frac{\sqrt{2}+1}{2}$

f) cos 195° = cos (90 + 60 + 45) = 1 + 1/2 + √2 / 2 = √2 + 3 / 2