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受欢迎的三角函数 >

cos(3θ)=sin(3θ)

解答

cos (3 θ) = sin (3 θ)

解答

θ = \frac{π}{12} + \frac{πn}{3}

+1

度数

θ = 1 5^{\circ} + 6 0^{\circ} n

求解步骤

cos (3 θ) = sin (3 θ)

使用三角恒等式改写

cos (3 θ) = sin (3 θ)

在两边除以

cos (3 θ), cos (3 θ) \neq = 0

\frac{cos ( 3 θ )}{cos ( 3 θ )} = \frac{sin ( 3 θ )}{cos ( 3 θ )}

化简

1 = \frac{sin ( 3 θ )}{cos ( 3 θ )}

使用基本三角恒等式:

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

1 = tan (3 θ)

交换两边

tan (3 θ) = 1

tan (3 θ) = 1

tan (3 θ) = 1

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}

3 θ = \frac{π}{4} + πn

3 θ = \frac{π}{4} + πn

解

3 θ = \frac{π}{4} + πn : θ = \frac{π}{12} + \frac{πn}{3}

3 θ = \frac{π}{4} + πn

两边除以

3

3 θ = \frac{π}{4} + πn

两边除以

3

\frac{3 θ}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3}

化简

\frac{3 θ}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3}

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

\frac{\frac{π}{4}}{3} + \frac{πn}{3} : \frac{π}{12} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 \cdot 3}

数字相乘:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{πn}{3}

θ = \frac{π}{12} + \frac{πn}{3}

θ = \frac{π}{12} + \frac{πn}{3}

θ = \frac{π}{12} + \frac{πn}{3}

θ = \frac{π}{12} + \frac{πn}{3}

作图

流行的例子

cos(5x)=1,0<= x<= pi/2

cos (5 x) = 1, 0 \leq x \leq \frac{π}{2}

sec(x)=-sqrt(1+tan(x))

sec (x) = - 1 + tan (x)

cos(2x)+2cos^2(x)=0

cos (2 x) + 2 cos^{2} (x) = 0

solvefor x,csc(x)+cot(x)=1

so l v e f or x, csc (x) + cot (x) = 1

sin (θ) = - 5