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受欢迎的三角函数 >

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

解答

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

解答

t = 1.23095 \dots + 2 πn, t = 2 π - 1.23095 \dots + 2 πn

+1

度数

t = 70.52877 \dots^{\circ} + 36 0^{\circ} n, t = 289.47122 \dots^{\circ} + 36 0^{\circ} n

求解步骤

2 (cos (t)) \cdot 2 - cos (t) - 1 = 0

化简

2 cos (t) \cdot 2 - cos (t) - 1 : 3 cos (t) - 1

2 cos (t) \cdot 2 - cos (t) - 1

数字相乘:

2 \cdot 2 = 4

= 4 cos (t) - cos (t) - 1

同类项相加:

4 cos (t) - cos (t) = 3 cos (t)

= 3 cos (t) - 1

3 cos (t) - 1 = 0

将

1

到右边

3 cos (t) - 1 = 0

两边加上

1

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

化简

3 cos (t) = 1

3 cos (t) = 1

两边除以

3

3 cos (t) = 1

两边除以

3

\frac{3 cos ( t )}{3} = \frac{1}{3}

化简

cos (t) = \frac{1}{3}

cos (t) = \frac{1}{3}

使用反三角函数性质

cos (t) = \frac{1}{3}

cos (t) = \frac{1}{3}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

t = arccos (\frac{1}{3}) + 2 πn, t = 2 π - arccos (\frac{1}{3}) + 2 πn

t = arccos (\frac{1}{3}) + 2 πn, t = 2 π - arccos (\frac{1}{3}) + 2 πn

以小数形式表示解

t = 1.23095 \dots + 2 πn, t = 2 π - 1.23095 \dots + 2 πn

作图

流行的例子

cos(c)=cos(7)cos(60)

cos (c) = cos (7) cos (6 0^{\circ})

cos(xpi)=(-1)^n

cos (x π) = (- 1)^{n}

3 csc (θ) = 4.5

cos^3(x)= 1/(4(3cos(x)+cos(3x)))

cos^{3} (x) = \frac{1}{4 ( 3 cos ( x ) + cos ( 3 x ) )}

solvefor w,s(t)=Ae^{-ct}cos(wt+θ)

so l v e f or w, s (t) = A e^{- c t} cos (wt + θ)