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受欢迎的三角函数 >

3cos(x)+5=7,0<= x<= 360

解答

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

解答

x = 0.84106 \dots, x = 36 0^{\circ} - 0.84106 \dots

+1

弧度

x = 0.84106 \dots, x = 2 π - 0.84106 \dots

求解步骤

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

将

5

到右边

3 cos (x) + 5 = 7

两边减去

5

3 cos (x) + 5 - 5 = 7 - 5

化简

3 cos (x) = 2

3 cos (x) = 2

两边除以

3

3 cos (x) = 2

两边除以

3

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

化简

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

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

使用反三角函数性质

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

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

的通解

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

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

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

在

0 \leq x \leq 36 0^{\circ}

范围内的解

x = arccos (\frac{2}{3}), x = 36 0^{\circ} - arccos (\frac{2}{3})

以小数形式表示解

x = 0.84106 \dots, x = 36 0^{\circ} - 0.84106 \dots

作图

流行的例子

cot(3x-6)=(sqrt(3))/3

cot (3 x - 6^{\circ}) = \frac{3}{3}

sqrt(1-cos(3x))=2pi

1 - cos (3 x) = 2 π

solvefor θ,r=(10)/(3+2cos(θ))

so l v e f or θ, r = \frac{10}{3 + 2 cos ( θ )}

sin(x)=(17.75)/(42)

sin (x) = \frac{17.75}{42}

3=20.39sin(θ)cos(θ)

3 = 20.39 sin (θ) cos (θ)