zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

-(15(0.5cos(x)-sin(x)))/((0.5sin(x)+cos(x))^2)=0

解答

- \frac{15 ( 0.5 cos ( x ) - sin ( x ) )}{( 0.5 sin ( x ) + cos ( x ) ) ^{2}} = 0

解答

x = 0.46364 \dots + πn

+1

度数

x = 26.56505 \dots^{\circ} + 18 0^{\circ} n

求解步骤

- \frac{15 ( 0.5 cos ( x ) - sin ( x ) )}{( 0.5 sin ( x ) + cos ( x ) ) ^{2}} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- (15 (0.5 cos (x) - sin (x))) = 0

使用三角恒等式改写

- (15 (0.5 cos (x) - sin (x))) = 0

在两边除以

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

\frac{- ( 15 ( 0.5 cos ( x ) - sin ( x ) ) )}{cos ( x )} = \frac{0}{cos ( x )}

化简

- 7.5 + \frac{15 sin ( x )}{cos ( x )} = 0

使用基本三角恒等式:

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

- 7.5 + 15 tan (x) = 0

- 7.5 + 15 tan (x) = 0

将

7.5

到右边

- 7.5 + 15 tan (x) = 0

两边加上

7.5

- 7.5 + 15 tan (x) + 7.5 = 0 + 7.5

化简

15 tan (x) = 7.5

15 tan (x) = 7.5

两边除以

15

15 tan (x) = 7.5

两边除以

15

\frac{15 tan ( x )}{15} = \frac{7.5}{15}

化简

tan (x) = 0.5

tan (x) = 0.5

使用反三角函数性质

tan (x) = 0.5

tan (x) = 0.5

的通解

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

x = arctan (0.5) + πn

x = arctan (0.5) + πn

以小数形式表示解

x = 0.46364 \dots + πn

作图

流行的例子

solvefor x,0.33=sin(209.42x)

so l v e f or x, 0.33 = sin (209.42 x)

- 2 + tan (θ) = - 1

sin^2(x)+cos^2(2/5)=1

sin^{2} (x) + cos^{2} (\frac{2}{5}) = 1

3 \cdot cos (4 θ) = 0

5 tan (x) - 5 = 0