若f(α)=[sin(π-α)cos(2π-α)tan(-α+π)]/[-tan(-α-π)sin(-π-α)]化简
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/02 01:33:15
若f(α)=[sin(π-α)cos(2π-α)tan(-α+π)]/[-tan(-α-π)sin(-π-α)]化简
若f(α)=[sin(π-α)cos(2π-α)tan(-α+π)]/[-tan(-α-π)sin(-π-α)]化简
若f(α)=[sin(π-α)cos(2π-α)tan(-α+π)]/[-tan(-α-π)sin(-π-α)]化简
f(α)=[sin(π-α)cos(2π-α)tan(-α+π)]/[-tan(-α-π)sin(-π-α)]
=[sinαcosα(-tanα)]/{tanα[-sin(π+α)}
=-sinαcosαtanα/(tanαsinα)
=-cosα
⑴
f(α) = [sin(π-α)cos(2π-α)tan(-π-α)]/sin(-π-α)
= [sin(α)cos(-α)tan(-α)]/sin(α)
= cos(-α)tan(-α)
= cos(-α) * sin(-α) / cos(-α)
= sin(-α)
= -s...
全部展开
⑴
f(α) = [sin(π-α)cos(2π-α)tan(-π-α)]/sin(-π-α)
= [sin(α)cos(-α)tan(-α)]/sin(α)
= cos(-α)tan(-α)
= cos(-α) * sin(-α) / cos(-α)
= sin(-α)
= -sin(α)
⑵
cos﹙α - 3π/2﹚=cos﹙-2π + π/2 + α ﹚= cos(π/2 + α) = -sin(α) =1/5
∴ f(α) = -sin(α) = 1/5
⑶
f(α) = -sin(α) = -sin(-1860°) = -sin(-5×360°- 60°) = -sin(-60°) = sin60°= √3/2
收起
利用三角函数的诱导公式的化简只需要记住一个口诀:奇变偶不变,符号看象限