Question

Calculați : sin 15°, cos 75°, sin 150°, cos 120°. sin 120°,cos 15°
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Answer 1

Răspuns:

Explicație pas cu pas:

a)cos30°=1-2sin²15°   ⇒   √3/2=1-2sin²15°     2sin²15°=1-√3/2

sin²15°=1/2-√3/4=(2-√3)/4        sin 15°=√2-√3/2

b)cos75°=cos(90°-15)=sin 15°=√2-√3/2

c)sin 150°=sin(180°-30°)=sin 30°=1/2

d)cos120°=cos(90°+30°)=sin 30°=1/2

e)sin 120°=sin(90°+30°)=-cos30°=-√3/2

f)cos15°=√1-sin²15°=√1-(2-√3)/4  =√(4-2+√3)/4=√2+√3/2