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受欢迎的三角函数 >

(cos(x)+5sin(x))/(2-3)=0

解答

\frac{cos ( x ) + 5 sin ( x )}{2 - 3} = 0

解答

x = - 0.19739 \dots + πn

+1

度数

x = - 11.30993 \dots^{\circ} + 18 0^{\circ} n

求解步骤

\frac{cos ( x ) + 5 sin ( x )}{2 - 3} = 0

使用三角恒等式改写

\frac{cos ( x ) + 5 sin ( x )}{2 - 3} = 0

在两边除以

cos (x), cos (x) \neq = 0

\frac{\frac{c o s ( x ) + 5 s i n ( x )}{2 - 3}}{cos ( x )} = \frac{0}{cos ( x )}

化简

- 1 - \frac{5 sin ( x )}{cos ( x )} = 0

使用基本三角恒等式:

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

- 1 - 5 tan (x) = 0

- 1 - 5 tan (x) = 0

将

1

到右边

- 1 - 5 tan (x) = 0

两边加上

1

- 1 - 5 tan (x) + 1 = 0 + 1

化简

- 5 tan (x) = 1

- 5 tan (x) = 1

两边除以

- 5

- 5 tan (x) = 1

两边除以

- 5

\frac{- 5 tan ( x )}{- 5} = \frac{1}{- 5}

化简

tan (x) = - \frac{1}{5}

tan (x) = - \frac{1}{5}

使用反三角函数性质

tan (x) = - \frac{1}{5}

tan (x) = - \frac{1}{5}

的通解

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

x = arctan (- \frac{1}{5}) + πn

x = arctan (- \frac{1}{5}) + πn

以小数形式表示解

x = - 0.19739 \dots + πn

作图

流行的例子

sin (y) = \frac{2}{3}

sin (a) = 0.6625

6-4cos^2(x)-9sin(x)=0

6 - 4 cos^{2} (x) - 9 sin (x) = 0

cos^2(x)+cos^2(3x)=1

cos^{2} (x) + cos^{2} (3 x) = 1

tan (x) = \frac{16}{3}