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受欢迎的三角函数 >

3cos(45)+4cos(y)=3

解答

3 cos (4 5^{\circ}) + 4 cos (y) = 3

解答

y = 1.34932 \dots + 36 0^{\circ} n, y = 36 0^{\circ} - 1.34932 \dots + 36 0^{\circ} n

+1

弧度

y = 1.34932 \dots + 2 πn, y = 2 π - 1.34932 \dots + 2 πn

求解步骤

3 cos (4 5^{\circ}) + 4 cos (y) = 3

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

使用以下普通恒等式:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{2}{2}

3 \cdot \frac{2}{2} + 4 cos (y) = 3

将

3 \frac{2}{2}

到右边

3 \cdot \frac{2}{2} + 4 cos (y) = 3

两边减去

3 \frac{2}{2}

3 \cdot \frac{2}{2} + 4 cos (y) - 3 \cdot \frac{2}{2} = 3 - 3 \cdot \frac{2}{2}

化简

3 \cdot \frac{2}{2} + 4 cos (y) - 3 \cdot \frac{2}{2} = 3 - 3 \cdot \frac{2}{2}

化简

3 \cdot \frac{2}{2} + 4 cos (y) - 3 \cdot \frac{2}{2} : 4 cos (y)

3 \cdot \frac{2}{2} + 4 cos (y) - 3 \cdot \frac{2}{2}

同类项相加:

3 \frac{2}{2} - 3 \frac{2}{2} = 0

= 4 cos (y)

化简

3 - 3 \cdot \frac{2}{2} : 3 - \frac{3 2}{2}

3 - 3 \cdot \frac{2}{2}

乘

3 \cdot \frac{2}{2} : \frac{3 2}{2}

3 \cdot \frac{2}{2}

分式相乘:

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

= \frac{2 \cdot 3}{2}

= 3 - \frac{3 2}{2}

4 cos (y) = 3 - \frac{3 2}{2}

4 cos (y) = 3 - \frac{3 2}{2}

4 cos (y) = 3 - \frac{3 2}{2}

两边除以

4

4 cos (y) = 3 - \frac{3 2}{2}

两边除以

4

\frac{4 cos ( y )}{4} = \frac{3}{4} - \frac{\frac{3 2}{2}}{4}

化简

\frac{4 cos ( y )}{4} = \frac{3}{4} - \frac{\frac{3 2}{2}}{4}

化简

\frac{4 cos ( y )}{4} : cos (y)

\frac{4 cos ( y )}{4}

数字相除:

\frac{4}{4} = 1

= cos (y)

化简

\frac{3}{4} - \frac{\frac{3 2}{2}}{4} : \frac{6 - 3 2}{8}

\frac{3}{4} - \frac{\frac{3 2}{2}}{4}

使用法则

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

= \frac{3 - \frac{3 2}{2}}{4}

化简

3 - \frac{3 2}{2} : \frac{6 - 3 2}{2}

3 - \frac{3 2}{2}

将项转换为分式:

3 = \frac{3 \cdot 2}{2}

= \frac{3 \cdot 2}{2} - \frac{3 2}{2}

因为分母相等，所以合并分式:

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

= \frac{3 \cdot 2 - 3 2}{2}

数字相乘:

3 \cdot 2 = 6

= \frac{6 - 3 2}{2}

= \frac{\frac{6 - 3 2}{2}}{4}

使用分式法则:

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

= \frac{6 - 3 2}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{6 - 3 2}{8}

cos (y) = \frac{6 - 3 2}{8}

cos (y) = \frac{6 - 3 2}{8}

cos (y) = \frac{6 - 3 2}{8}

使用反三角函数性质

cos (y) = \frac{6 - 3 2}{8}

cos (y) = \frac{6 - 3 2}{8}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

y = arccos (\frac{6 - 3 2}{8}) + 36 0^{\circ} n, y = 36 0^{\circ} - arccos (\frac{6 - 3 2}{8}) + 36 0^{\circ} n

y = arccos (\frac{6 - 3 2}{8}) + 36 0^{\circ} n, y = 36 0^{\circ} - arccos (\frac{6 - 3 2}{8}) + 36 0^{\circ} n

以小数形式表示解

y = 1.34932 \dots + 36 0^{\circ} n, y = 36 0^{\circ} - 1.34932 \dots + 36 0^{\circ} n

作图

流行的例子

cos(3θ)=cos(θ)

cos (3 θ) = cos (θ)

(tan(x)-sec(x))^2=3

(tan (x) - sec (x))^{2} = 3

solvefor y,ln(x^2+10)+csc(y)=c

so l v e f or y, ln (x^{2} + 10) + csc (y) = c

sin (a) = \frac{7}{15}

(3sqrt(3))/(14)=sin(x)

\frac{3 3}{14} = sin (x)