1. 角度与弧度的转换：
– 1弧度 = π/180度
– 1度 = π/180弧度
2. 正弦、余弦和正切的相互转换：
– sin(θ) = sin(π/4 + (90° – θ))
– cos(θ) = cos(π/4 + (90° – θ))
– tan(θ) = tan(π/4 + (90° – θ))
3. 特殊角的三角函数值：
– sin(0°) = 0
– cos(0°) = 1
– tan(0°) = 0
– sin(π/2) = cos(π/2) = 1
– cos(π/2) = -sin(π/2) = 0
– tan(π/2) = -1
4. 三角函数的周期性：
– sin(x) = sin(x + 2kπ) for any integer k
– cos(x) = cos(x + 2kπ) for any integer k
– tan(x) = tan(x + 2kπ) for any integer k
– sec(x) = sec(x + 2kπ) for any integer k
– csc(x) = csc(x + 2kπ) for any integer k
5. 三角函数的和差化积公式：
– sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
– cos(A + B) = cos(A)cos(B) – sin(A)sin(B)
– tan(A + B) = sqrt(tan(A)² + tan(B)²)
– sec(A + B) = sec(A)cos(B) + cos(A)sin(B)
– csc(A + B) = csc(A)cos(B) – sin(A)sin(B)
6. 三角函数的积化和差公式：
– sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
– cos(A + B) = cos(A)cos(B) – sin(A)sin(B)
– tan(A + B) = sqrt(tan(A)² + tan(B)²)
– sec(A + B) = sec(A)cos(B) + cos(A)sin(B)
– csc(A + B) = csc(A)cos(B) – sin(A)sin(B)
7. 三角函数的辅助角公式：
– sin(α + β) = sin(α)cos(β) + cos(α)sin(β)
– cos(α + β) = cos(α)cos(β) – sin(α)sin(β)
– tan(α + β) = tan(α)cos(β) + sin(α)sin(β)
– sec(α + β) = sec(α)cos(β) + cos(α)sin(β)
– csc(α + β) = csc(α)cos(β) – sin(α)sin(β)
通过熟练掌握这些基本换算方法和技巧，你可以更加高效地解决涉及三角函数的问题。记住，理解和应用这些公式需要时间和练习，但一旦掌握了，你会发现自己在处理相关数学问题时会更加得心应手。