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受欢迎的三角函数 >

5sin(3x)=4

解答

5 sin (3 x) = 4

解答

x = \frac{0.92729 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{3} + \frac{2 πn}{3}

+1

度数

x = 17.71003 \dots^{\circ} + 12 0^{\circ} n, x = 42.28996 \dots^{\circ} + 12 0^{\circ} n

求解步骤

5 sin (3 x) = 4

两边除以

5

5 sin (3 x) = 4

两边除以

5

\frac{5 sin ( 3 x )}{5} = \frac{4}{5}

化简

sin (3 x) = \frac{4}{5}

sin (3 x) = \frac{4}{5}

使用反三角函数性质

sin (3 x) = \frac{4}{5}

sin (3 x) = \frac{4}{5}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

3 x = arcsin (\frac{4}{5}) + 2 πn, 3 x = π - arcsin (\frac{4}{5}) + 2 πn

3 x = arcsin (\frac{4}{5}) + 2 πn, 3 x = π - arcsin (\frac{4}{5}) + 2 πn

解

3 x = arcsin (\frac{4}{5}) + 2 πn : x = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

3 x = arcsin (\frac{4}{5}) + 2 πn

两边除以

3

3 x = arcsin (\frac{4}{5}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

化简

x = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

解

3 x = π - arcsin (\frac{4}{5}) + 2 πn : x = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

3 x = π - arcsin (\frac{4}{5}) + 2 πn

两边除以

3

3 x = π - arcsin (\frac{4}{5}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

化简

x = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

x = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

x = \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{arcsin ( \frac{4}{5} )}{3} + \frac{2 πn}{3}

以小数形式表示解

x = \frac{0.92729 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} - \frac{0.92729 \dots}{3} + \frac{2 πn}{3}

作图

流行的例子

sec(θ)= 1/(cos(67.38))

sec (θ) = \frac{1}{cos ( 67.3 8 ^{\circ} )}

cos (x) = \frac{15}{19}

(sec(x)+1)^2-tan(x)=0

(sec (x) + 1)^{2} - tan (x) = 0

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sec (θ) = \frac{6}{- 5}, sec (- θ)