已知角α的正切值为b/a,求角α的正弦值和余弦值

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已知角α的正切值为b/a,求角α的正弦值和余弦值已知角α的正切值为b/a,求角α的正弦值和余弦值已知角α的正切值为b/a,求角α的正弦值和余弦值tanα=b/a,则(tanα)^2=b^2/a^2=(

已知角α的正切值为b/a,求角α的正弦值和余弦值
已知角α的正切值为b/a,求角α的正弦值和余弦值

已知角α的正切值为b/a,求角α的正弦值和余弦值
tanα=b/a,则(tanα)^2=b^2/a^2=(sinα)^2/(cosα)^2=[1-(cosα)^2]/(cosα)^2,可知,
(cosα)^2=1/[1+(tanα)^2].最后求得:cosα=|根号下(1/[1+b^2/a^2)]|,
同理,(tanα)^2=b^2/a^2=(sinα)^2/(cosα)^2=(sinα)^2/[1-(sinα)^2],可知,
(sinα)^2=1+1/(tanα)^2.最后求得:sinα=|根号下(1+a^2/b^2)|.
因为,a,b正负未知,所以要加上绝对值.

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