求下列各三角函数值 (1)sin105度 (2)cos165度 (3)sin5派/12

问题描述:

求下列各三角函数值 (1)sin105度 (2)cos165度 (3)sin5派/12


⑴sin105°=sin﹙60°+45°﹚
=sin60°cos45°+cos60°sin45°
=﹙√3/2﹚﹙√2/2﹚+﹙1/2﹚﹙√2/2﹚
=﹙√6/4﹚+﹙√2/4﹚
=﹙√ 6+√2﹚/4
⑵cos165°=cos﹙180°-15°﹚
=-cos15°
=-cos﹙45°-30°﹚
=-﹙cos45°cos30°+sin45°sin30°﹚
=-[﹙√2/2﹚﹙√3/2﹚+﹙√2/2﹚﹙1/2﹚]
=-﹙√6+√2﹚/4
⑶sin5派/12 =sin75°
=sin﹙30°+45°﹚
=sin30°cos45°+cos30°sin45°
=﹙1/2﹚﹙√2/2﹚+﹙√3/2﹚﹙√2/2﹚
=﹙√6+√2﹚/4