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受欢迎的三角函数 >

2sin(t)cos(t)+sin(t)-2cos(t)-1=0

解答

2 sin (t) cos (t) + sin (t) - 2 cos (t) - 1 = 0

解答

t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn, t = \frac{π}{2} + 2 πn

+1

度数

t = 12 0^{\circ} + 36 0^{\circ} n, t = 24 0^{\circ} + 36 0^{\circ} n, t = 9 0^{\circ} + 36 0^{\circ} n

求解步骤

2 sin (t) cos (t) + sin (t) - 2 cos (t) - 1 = 0

分解

2 sin (t) cos (t) + sin (t) - 2 cos (t) - 1 : (2 cos (t) + 1) (sin (t) - 1)

2 sin (t) cos (t) + sin (t) - 2 cos (t) - 1

= (2 sin (t) cos (t) + sin (t)) + (- 2 cos (t) - 1)

从

- 2 cos (t) - 1

分解出因式

- 1

:

- (2 cos (t) + 1)

- 2 cos (t) - 1

因式分解出通项

- 1

= - (2 cos (t) + 1)

从

2 sin (t) cos (t) + sin (t)

分解出因式

sin (t)

:

sin (t) (2 cos (t) + 1)

2 sin (t) cos (t) + sin (t)

因式分解出通项

sin (t)

= sin (t) (2 cos (t) + 1)

= - (2 cos (t) + 1) + sin (t) (2 cos (t) + 1)

因式分解出通项

2 cos (t) + 1

= (2 cos (t) + 1) (sin (t) - 1)

(2 cos (t) + 1) (sin (t) - 1) = 0

分别求解每个部分

2 cos (t) + 1 = 0 or sin (t) - 1 = 0

2 cos (t) + 1 = 0 : t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn

2 cos (t) + 1 = 0

将

1

到右边

2 cos (t) + 1 = 0

两边减去

1

2 cos (t) + 1 - 1 = 0 - 1

化简

2 cos (t) = - 1

2 cos (t) = - 1

两边除以

2

2 cos (t) = - 1

两边除以

2

\frac{2 cos ( t )}{2} = \frac{- 1}{2}

化简

cos (t) = - \frac{1}{2}

cos (t) = - \frac{1}{2}

cos (t) = - \frac{1}{2}

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}

t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn

t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn

sin (t) - 1 = 0 : t = \frac{π}{2} + 2 πn

sin (t) - 1 = 0

将

1

到右边

sin (t) - 1 = 0

两边加上

1

sin (t) - 1 + 1 = 0 + 1

化简

sin (t) = 1

sin (t) = 1

sin (t) = 1

的通解

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

t = \frac{π}{2} + 2 πn

t = \frac{π}{2} + 2 πn

合并所有解

t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn, t = \frac{π}{2} + 2 πn

作图

流行的例子

4cos^2(x/2)-3=0

4 cos^{2} (\frac{x}{2}) - 3 = 0

sin(2θ)+cos(θ)=0,0<= θ<= 2pi

sin (2 θ) + cos (θ) = 0, 0 \leq θ \leq 2 π

sin(10)=2sin(a)cos(a)

sin (1 0^{\circ}) = 2 sin (a) cos (a)

cos^2(x)=2+2sin(x),0<= x<= 2pi

cos^{2} (x) = 2 + 2 sin (x), 0 \leq x \leq 2 π

cos^{2} (x) = \frac{3}{5}