Question

求值:

(1)sin315°sin(-1 260°)+cos570°sin(-840°);

(2)已知tan(π+α)=3,求

的值.

Answer 1

解析:(1)原式=sin(360°-45°)sin(-4×360°+180°)+cos(360°+210°)(-sin840°)

=-sin45°sin180°-cos(180°+30°)sin(2×360°+120°)

=-×0+cos30°sin(180°-60°)

=cos30°sin60°=.

(2)∵tan(π+α)=3,∴tanα=3.

原式====7.

点评:熟记诱导公式和特殊角的三角函数值,求三角函数值时要特别注意符号问题.较复杂的求值问题要先化简再求值.