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受欢迎的三角函数 >

0.7sin(3pit)-3picos(3pit)=0

解答

0.7 sin (3 π t) - 3 π cos (3 π t) = 0

解答

t = \frac{1.49666 \dots}{9.42477 \dots} + \frac{πn}{9.42477 \dots}

+1

度数

t = 9.09860 \dots^{\circ} + 19.09859 \dots^{\circ} n

求解步骤

0.7 sin (3 π t) - 3 π cos (3 π t) = 0

使用三角恒等式改写

0.7 sin (3 π t) - 3 π cos (3 π t) = 0

在两边除以

cos (3 π t), cos (3 π t) \neq = 0

\frac{0.7 sin ( 3 π t ) - 3 π cos ( 3 π t )}{cos ( 3 π t )} = \frac{0}{cos ( 3 π t )}

化简

\frac{0.7 sin ( 9.42477 \dots t )}{cos ( 9.42477 \dots t )} - 9.42477 \dots = 0

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

0.7 tan (9.42477 \dots t) - 9.42477 \dots = 0

0.7 tan (9.42477 \dots t) - 9.42477 \dots = 0

将

9.42477 \dots

到右边

0.7 tan (9.42477 \dots t) - 9.42477 \dots = 0

两边加上

9.42477 \dots

0.7 tan (9.42477 \dots t) - 9.42477 \dots + 9.42477 \dots = 0 + 9.42477 \dots

化简

0.7 tan (9.42477 \dots t) = 9.42477 \dots

0.7 tan (9.42477 \dots t) = 9.42477 \dots

两边除以

0.7

0.7 tan (9.42477 \dots t) = 9.42477 \dots

两边除以

0.7

\frac{0.7 tan ( 9.42477 \dots t )}{0.7} = \frac{9.42477 \dots}{0.7}

化简

tan (9.42477 \dots t) = 13.46396 \dots

tan (9.42477 \dots t) = 13.46396 \dots

使用反三角函数性质

tan (9.42477 \dots t) = 13.46396 \dots

tan (9.42477 \dots t) = 13.46396 \dots

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

9.42477 \dots t = arctan (13.46396 \dots) + πn

9.42477 \dots t = arctan (13.46396 \dots) + πn

解

9.42477 \dots t = arctan (13.46396 \dots) + πn : t = \frac{arctan ( 13.46396 \dots )}{9.42477 \dots} + \frac{πn}{9.42477 \dots}

9.42477 \dots t = arctan (13.46396 \dots) + πn

两边除以

9.42477 \dots

9.42477 \dots t = arctan (13.46396 \dots) + πn

两边除以

9.42477 \dots

\frac{9.42477 \dots t}{9.42477 \dots} = \frac{arctan ( 13.46396 \dots )}{9.42477 \dots} + \frac{πn}{9.42477 \dots}

化简

t = \frac{arctan ( 13.46396 \dots )}{9.42477 \dots} + \frac{πn}{9.42477 \dots}

t = \frac{arctan ( 13.46396 \dots )}{9.42477 \dots} + \frac{πn}{9.42477 \dots}

t = \frac{arctan ( 13.46396 \dots )}{9.42477 \dots} + \frac{πn}{9.42477 \dots}

以小数形式表示解

t = \frac{1.49666 \dots}{9.42477 \dots} + \frac{πn}{9.42477 \dots}

作图

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