高三文科数学[三角函数[1.ppt
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综合运用三角公式进行三角变换,常用的变换:变换角度,变换名称,变换解析式结构.
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例1
已知
求cos(β-α)的值.
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所以
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已知sinα+sinβ= ,
cosα+cosβ= ,求cos(α-β)的值.
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求sinx+cosx、sinx-cosx、sinxcosx的值是常规问题,知一推三,平方、活用公式是化简、求值常用的方法,也可联立sin2x+cos2x=1,求出sinx、cosx的值后再进行解决.
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例3
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已知:α是第一象限的角,
且cosα= ,
则 的值为 .
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三角恒等变形的实质是对角、函数名称及运算结构的转化,统一角度,统一函数名,化切为弦,化弦为切,都是常用的恒等变换的技巧。
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