高中必修四数学的主要公式

高中必修四数学的主要公式

高中必修四数学的主要公式如下：
1. 乘法与因式分解
- a^2 - b^2 = (a + b)(a - b)
- a^3 + b^3 = (a + b)(a^2 - ab + b^2)
- a^3 - b^3 = (a - b)(a^2 + ab + b^2)
2. 三角不等式
- |a + b| ≤ |a| + |b|
- |a - b| ≤ |a| + |b|
- |a| ≤ b ↔ -b ≤ a ≤ b
- |a - b| ≥ |a| - |b|
3. 一元二次方程的解
- x1, x2 = (-b ± √(b^2 - 4ac)) / (2a)
- Δ = b^2 - 4ac
- Δ = 0 ↔ 方程有两个相等的实根
- Δ > 0 ↔ 方程有两个不等的实根
- Δ < 0 ↔ 方程没有实根，有共轭复数根
4. 三角函数公式
- sin(A + B) = sinAcosB + cosAsinB
- sin(A - B) = sinAcosB - cosAsinB
- cos(A + B) = cosAcosB - sinAsinB
- cos(A - B) = cosAcosB + sinAsinB
- tan(A + B) = (tanA + tanB) / (1 - tanAtanB)
- tan(A - B) = (tanA - tanB) / (1 + tanAtanB)
- cot(A + B) = (cotAcotB - 1) / (cotB + cotA)
- cot(A - B) = (cotAcotB + 1) / (cotB - cotA)
5. 三角函数的和差化积
- sinA + sinB = 2sin((A + B)/2)cos((A - B)/2)
- sinA - sinB = 2cos((A + B)/2)sin((A - B)/2)
- cosA + cosB = 2cos((A + B)/2)cos((A - B)/2)
- cosA - cosB = -2sin((A + B)/2)sin((A - B)/2)
6. 数列前n项和
- 1 + 2 + 3 + ... + n = n(n + 1)/2
- 1 + 3 + 5 + ... + (2n - 1) = n^2
- 2 + 4 + 6 + ... + (2n) = n(n + 1)
- 1^2 + 2^2 + 3^2 + ... + n^2 = n(n + 1)(2n + 1)/6
- 1^3 + 2^3 + 3^3 + ... + n^3 = n^2(n + 1)/2
7. 立体几何公式
- S = ch
- S = c'h
- S = 1/2ch
- S = 1/2(c + c')l
- S = 4πr^2
- S = 2πrh
- V = 1/3Sh
- V = 1/3πr^2h
- V = Sh/3
8. 诱导公式
- sin(2kπ + α) = sinα
- cos(2kπ + α) = cosα
- tan(2kπ + α) = tanα
- cot(2kπ + α) = cotα
- sin(π + α) = -sinα
- cos(π + α) = -cosα
- tan(π + α) = -tanα
- cot(π + α) = -cotα
- sin(-α) = -sinα
- cos(-α) = cosα
- tan(-α) = -tanα
- cot(-α) = -cotα
以上是高中必修四数学的主要公式，希望对您有所帮助。2024-11-09