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受欢迎的三角函数 >

sin^2(a)=3cos^2(a)

解答

sin^{2} (a) = 3 cos^{2} (a)

解答

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

+1

度数

a = 12 0^{\circ} + 18 0^{\circ} n, a = 6 0^{\circ} + 18 0^{\circ} n

求解步骤

sin^{2} (a) = 3 cos^{2} (a)

两边减去

3 cos^{2} (a)

sin^{2} (a) - 3 cos^{2} (a) = 0

分解

sin^{2} (a) - 3 cos^{2} (a) : (sin (a) + 3 cos (a)) (sin (a) - 3 cos (a))

sin^{2} (a) - 3 cos^{2} (a)

将

sin^{2} (a) - 3 cos^{2} (a)

改写为

sin^{2} (a) - (3 cos (a))^{2}

sin^{2} (a) - 3 cos^{2} (a)

使用根式运算法则:

a = (a)^{2}

3 = (3)^{2}

= sin^{2} (a) - (3)^{2} cos^{2} (a)

使用指数法则:

a^{m} b^{m} = (ab)^{m}

(3)^{2} cos^{2} (a) = (3 cos (a))^{2}

= sin^{2} (a) - (3 cos (a))^{2}

= sin^{2} (a) - (3 cos (a))^{2}

使用平方差公式:

x^{2} - y^{2} = (x + y) (x - y)

sin^{2} (a) - (3 cos (a))^{2} = (sin (a) + 3 cos (a)) (sin (a) - 3 cos (a))

= (sin (a) + 3 cos (a)) (sin (a) - 3 cos (a))

(sin (a) + 3 cos (a)) (sin (a) - 3 cos (a)) = 0

分别求解每个部分

sin (a) + 3 cos (a) = 0 or sin (a) - 3 cos (a) = 0

sin (a) + 3 cos (a) = 0 : a = \frac{2 π}{3} + πn

sin (a) + 3 cos (a) = 0

使用三角恒等式改写

sin (a) + 3 cos (a) = 0

在两边除以

cos (a), cos (a) \neq = 0

\frac{sin ( a ) + 3 cos ( a )}{cos ( a )} = \frac{0}{cos ( a )}

化简

\frac{sin ( a )}{cos ( a )} + 3 = 0

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (a) + 3 = 0

tan (a) + 3 = 0

将

3

到右边

tan (a) + 3 = 0

两边减去

3

tan (a) + 3 - 3 = 0 - 3

化简

tan (a) = - 3

tan (a) = - 3

tan (a) = - 3

的通解

tan (x)

周期表（周期为

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

a = \frac{2 π}{3} + πn

a = \frac{2 π}{3} + πn

sin (a) - 3 cos (a) = 0 : a = \frac{π}{3} + πn

sin (a) - 3 cos (a) = 0

使用三角恒等式改写

sin (a) - 3 cos (a) = 0

在两边除以

cos (a), cos (a) \neq = 0

\frac{sin ( a ) - 3 cos ( a )}{cos ( a )} = \frac{0}{cos ( a )}

化简

\frac{sin ( a )}{cos ( a )} - 3 = 0

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (a) - 3 = 0

tan (a) - 3 = 0

将

3

到右边

tan (a) - 3 = 0

两边加上

3

tan (a) - 3 + 3 = 0 + 3

化简

tan (a) = 3

tan (a) = 3

tan (a) = 3

的通解

tan (x)

周期表（周期为

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

a = \frac{π}{3} + πn

a = \frac{π}{3} + πn

合并所有解

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

作图

流行的例子

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3 cot (x) + 3 = 0

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