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受欢迎的三角函数 >

8/(sin(38))= 6/(sin(a))

解答

\frac{8}{sin ( 3 8 ^{\circ} )} = \frac{6}{sin ( a )}

解答

a = 0.47996 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.47996 \dots + 36 0^{\circ} n

+1

弧度

a = 0.47996 \dots + 2 πn, a = π - 0.47996 \dots + 2 πn

求解步骤

\frac{8}{sin ( 3 8 ^{\circ} )} = \frac{6}{sin ( a )}

使用分式交叉相乘

\frac{8}{sin ( 3 8 ^{\circ} )} = \frac{6}{sin ( a )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

8 sin (a) = sin (3 8^{\circ}) \cdot 6

8 sin (a) = sin (3 8^{\circ}) \cdot 6

两边除以

8

8 sin (a) = sin (3 8^{\circ}) \cdot 6

两边除以

8

\frac{8 sin ( a )}{8} = \frac{sin ( 3 8 ^{\circ} ) \cdot 6}{8}

化简

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

验证解

找到无定义的点（奇点）:

sin (a) = 0

取

\frac{6}{sin ( a )}

的分母，令其等于零

sin (a) = 0

以下点无定义

sin (a) = 0

将不在定义域的点与解相综合:

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

使用反三角函数性质

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

sin (a) = \frac{3 sin ( 3 8 ^{\circ} )}{4}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

a = arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n

a = arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{3 sin ( 3 8 ^{\circ} )}{4}) + 36 0^{\circ} n

以小数形式表示解

a = 0.47996 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.47996 \dots + 36 0^{\circ} n

作图

流行的例子

sin(x)=(-sqrt(3))/2 ,270<x<360

sin (x) = \frac{- 3}{2}, 27 0^{\circ} < x < 36 0^{\circ}

solvefor x,R=(v^2sin(2x))/g

so l v e f or x, R = \frac{v ^{2} sin ( 2 x )}{g}

sin(θ)csc(3θ-40)=1,calculetan(3θ)

sin (θ) csc (3 θ - 40) = 1, c a l c u l e tan (3 θ)

cos^2(x)+5cos(x)-6=0

cos^{2} (x) + 5 cos (x) - 6 = 0

solvefor x,sin(x)=-7/25

so l v e f or x, sin (x) = - \frac{7}{25}