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受欢迎的三角函数 >

-1+sin^2(a)+cos^2(a)=cos^2(a)

解答

- 1 + sin^{2} (a) + cos^{2} (a) = cos^{2} (a)

解答

a = \frac{π}{2} + 2 πn, a = \frac{3 π}{2} + 2 πn

+1

度数

a = 9 0^{\circ} + 36 0^{\circ} n, a = 27 0^{\circ} + 36 0^{\circ} n

求解步骤

- 1 + sin^{2} (a) + cos^{2} (a) = cos^{2} (a)

使用三角恒等式改写

- 1 + sin^{2} (a) + cos^{2} (a)

使用毕达哥拉斯恒等式:

cos^{2} (x) + sin^{2} (x) = 1

= - 1 + 1

- 1 + 1 = cos^{2} (a)

交换两边

cos^{2} (a) = - 1 + 1

数字相加/相减:

- 1 + 1 = 0

cos^{2} (a) = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

cos (a) = 0

cos (a) = 0

的通解

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

a = \frac{π}{2} + 2 πn, a = \frac{3 π}{2} + 2 πn

a = \frac{π}{2} + 2 πn, a = \frac{3 π}{2} + 2 πn

作图

流行的例子

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sin (2 x) = \frac{3}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

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