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受欢迎的三角函数 >

(6.7)/(sin(33))=(5.4)/(sin(A))

解答

\frac{6.7}{sin ( 3 3 ^{\circ} )} = \frac{5.4}{sin ( A )}

解答

A = 0.45444 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.45444 \dots + 36 0^{\circ} n

+1

弧度

A = 0.45444 \dots + 2 πn, A = π - 0.45444 \dots + 2 πn

求解步骤

\frac{6.7}{sin ( 3 3 ^{\circ} )} = \frac{5.4}{sin ( A )}

使用分式交叉相乘

\frac{6.7}{sin ( 3 3 ^{\circ} )} = \frac{5.4}{sin ( A )}

使用分式交叉相乘: 若

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

则

a \cdot d = b \cdot c

6.7 sin (A) = sin (3 3^{\circ}) \cdot 5.4

6.7 sin (A) = sin (3 3^{\circ}) \cdot 5.4

两边除以

6.7

6.7 sin (A) = sin (3 3^{\circ}) \cdot 5.4

两边除以

6.7

\frac{6.7 sin ( A )}{6.7} = \frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

化简

sin (A) = \frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

sin (A) = \frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

验证解

找到无定义的点（奇点）:

sin (A) = 0

取

\frac{5.4}{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{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

使用反三角函数性质

sin (A) = \frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}

sin (A) = \frac{sin ( 3 3 ^{\circ} ) 5.4}{6.7}

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{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}) + 36 0^{\circ} n

A = arcsin (\frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}) + 36 0^{\circ} n, A = 18 0^{\circ} - arcsin (\frac{sin ( 3 3 ^{\circ} ) \cdot 5.4}{6.7}) + 36 0^{\circ} n

以小数形式表示解

A = 0.45444 \dots + 36 0^{\circ} n, A = 18 0^{\circ} - 0.45444 \dots + 36 0^{\circ} n

作图

流行的例子

2 - 3 sin (θ) = 0

cos (x) = - 0.83

solvefor y,x=cot(y)

so l v e f or y, x = cot (y)

solvefor x,2cos((pix)/3)=1

so l v e f or x, 2 cos (\frac{π x}{3}) = 1

cos (x) = - 0.16