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求75°的三角函数值是在高中《代数》应用两角和差公式求值的.我们应该引导学生应用数形结合的思想用构图的方法来求75°的三角函数值,这样有利于培养学生应用知以分析问题和解决问题的能力.下面介绍八种求法,为了节省篇幅,每种解法求一种或两种三角函数值. 解法1:如图1所示,△ABC中,∠C=90°,∠BDC=30°.∠A=15°,则∠ABC=75°,设BC=1,则AD=DB=2,DC=3~(1/2),AC=2+3~(1/2),故tg75°=2+3~(1/2).
Finding the trigonometric function value of 75° is evaluated in the algebra of high school using the two-corner and difference formulas. We should guide students to apply the combination of number and shape to use the composition method to find the trigonometric function value of 75°, which is conducive to cultivating. Students apply the ability to understand problems and solve problems. The following eight methods are introduced. To save space, each solution requires one or two trigonometric functions. Solution 1: As shown in Figure 1, △ABC, ∠C =90°, ∠BDC=30°. ∠A=15°, then ∠ABC=75°, set BC=1, then AD=DB=2, DC=3~(1/2), AC=2+3 ~(1/2), so tg75°=2+3~(1/2).