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受欢迎的三角函数 >

cos^2(θ)= 49/64

解答

cos^{2} (θ) = \frac{49}{64}

解答

θ = 0.50536 \dots + 2 πn, θ = 2 π - 0.50536 \dots + 2 πn, θ = 2.63623 \dots + 2 πn, θ = - 2.63623 \dots + 2 πn

+1

度数

θ = 28.95502 \dots^{\circ} + 36 0^{\circ} n, θ = 331.04497 \dots^{\circ} + 36 0^{\circ} n, θ = 151.04497 \dots^{\circ} + 36 0^{\circ} n, θ = - 151.04497 \dots^{\circ} + 36 0^{\circ} n

求解步骤

cos^{2} (θ) = \frac{49}{64}

用替代法求解

cos^{2} (θ) = \frac{49}{64}

令

: cos (θ) = u

u^{2} = \frac{49}{64}

u^{2} = \frac{49}{64} : u = \frac{7}{8}, u = - \frac{7}{8}

u^{2} = \frac{49}{64}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{49}{64}, u = - \frac{49}{64}

\frac{49}{64} = \frac{7}{8}

\frac{49}{64}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{49}{64}

64 = 8

64

因式分解数字:

64 = 8^{2}

= 8^{2}

使用根式运算法则:

n a^{n} = a

8^{2} = 8

= 8

= \frac{49}{8}

49 = 7

49

因式分解数字:

49 = 7^{2}

= 7^{2}

使用根式运算法则:

n a^{n} = a

7^{2} = 7

= 7

= \frac{7}{8}

- \frac{49}{64} = - \frac{7}{8}

- \frac{49}{64}

化简

\frac{49}{64} : \frac{7}{8}

\frac{49}{64}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{49}{64}

64 = 8

64

因式分解数字:

64 = 8^{2}

= 8^{2}

使用根式运算法则:

n a^{n} = a

8^{2} = 8

= 8

= \frac{49}{8}

49 = 7

49

因式分解数字:

49 = 7^{2}

= 7^{2}

使用根式运算法则:

n a^{n} = a

7^{2} = 7

= 7

= \frac{7}{8}

= - \frac{7}{8}

u = \frac{7}{8}, u = - \frac{7}{8}

u = cos (θ)

代回

cos (θ) = \frac{7}{8}, cos (θ) = - \frac{7}{8}

cos (θ) = \frac{7}{8}, cos (θ) = - \frac{7}{8}

cos (θ) = \frac{7}{8} : θ = arccos (\frac{7}{8}) + 2 πn, θ = 2 π - arccos (\frac{7}{8}) + 2 πn

cos (θ) = \frac{7}{8}

使用反三角函数性质

cos (θ) = \frac{7}{8}

cos (θ) = \frac{7}{8}

的通解

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

θ = arccos (\frac{7}{8}) + 2 πn, θ = 2 π - arccos (\frac{7}{8}) + 2 πn

θ = arccos (\frac{7}{8}) + 2 πn, θ = 2 π - arccos (\frac{7}{8}) + 2 πn

cos (θ) = - \frac{7}{8} : θ = arccos (- \frac{7}{8}) + 2 πn, θ = - arccos (- \frac{7}{8}) + 2 πn

cos (θ) = - \frac{7}{8}

使用反三角函数性质

cos (θ) = - \frac{7}{8}

cos (θ) = - \frac{7}{8}

的通解

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

θ = arccos (- \frac{7}{8}) + 2 πn, θ = - arccos (- \frac{7}{8}) + 2 πn

θ = arccos (- \frac{7}{8}) + 2 πn, θ = - arccos (- \frac{7}{8}) + 2 πn

合并所有解

θ = arccos (\frac{7}{8}) + 2 πn, θ = 2 π - arccos (\frac{7}{8}) + 2 πn, θ = arccos (- \frac{7}{8}) + 2 πn, θ = - arccos (- \frac{7}{8}) + 2 πn

以小数形式表示解

θ = 0.50536 \dots + 2 πn, θ = 2 π - 0.50536 \dots + 2 πn, θ = 2.63623 \dots + 2 πn, θ = - 2.63623 \dots + 2 πn

作图

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