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受欢迎的三角函数 >

cos(θ)= 3/(sqrt(45))

解答

cos (θ) = \frac{3}{45}

解答

θ = 1.10714 \dots + 2 πn, θ = 2 π - 1.10714 \dots + 2 πn

+1

弧度

θ = 1.10714 \dots + 6.28318 \dots n, θ = 5.17603 \dots + 6.28318 \dots n

求解步骤

cos (θ) = \frac{3}{45}

化简

\frac{3}{45} : \frac{5}{5}

\frac{3}{45}

分解

45 : 35

因式分解

45 = 3^{2} \cdot 5

= 3^{2} \cdot 5

使用根式运算法则:

n ab = n a n b

= 5 3^{2}

化简

3^{2} : 3

3^{2}

使用根式运算法则:

n a^{n} = a,

假定

a \geq 0

= 3

= 35

= \frac{3}{3 5}

数字相除:

\frac{3}{3} = 1

= \frac{1}{5}

\frac{1}{5}

有理化:

\frac{5}{5}

\frac{1}{5}

乘以共轭根式

\frac{5}{5}

= \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

使用根式运算法则:

a a = a

55 = 5

= 5

= \frac{5}{5}

= \frac{5}{5}

cos (θ) = \frac{5}{5}

使用反三角函数性质

cos (θ) = \frac{5}{5}

cos (θ) = \frac{5}{5}

的通解

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

θ = arccos (\frac{5}{5}) + 2 πn, θ = 2 π - arccos (\frac{5}{5}) + 2 πn

θ = arccos (\frac{5}{5}) + 2 πn, θ = 2 π - arccos (\frac{5}{5}) + 2 πn

以小数形式表示解

θ = 1.10714 \dots + 2 πn, θ = 2 π - 1.10714 \dots + 2 πn

作图

流行的例子

cos^{2} (x) = \frac{9}{16}

sin (4 x) = 0.5

3cos^2(x)+6cos(x)=-3,0<= x<= 2pi

3 cos^{2} (x) + 6 cos (x) = - 3, 0 \leq x \leq 2 π

tan(θ)=7,sec^2(θ)

tan (θ) = 7, sec^{2} (θ)

4cos(x-45)+7=10,0<= x<= 360

4 cos (x - 4 5^{\circ}) + 7 = 10, 0^{\circ} \leq x \leq 36 0^{\circ}