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受欢迎的三角函数 >

2sin(x)=5cos(x),0<= x<360

解答

2 sin (x) = 5 cos (x), 0^{\circ} \leq x < 36 0^{\circ}

解答

x = 1.19028 \dots, x = 1.19028 \dots + 18 0^{\circ}

+1

弧度

x = 1.19028 \dots, x = 1.19028 \dots + π

求解步骤

2 sin (x) = 5 cos (x), 0^{\circ} \leq x < 36 0^{\circ}

使用三角恒等式改写

2 sin (x) = 5 cos (x)

在两边除以

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

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

化简

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

使用基本三角恒等式:

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

2 tan (x) = 5

2 tan (x) = 5

两边除以

2

2 tan (x) = 5

两边除以

2

\frac{2 tan ( x )}{2} = \frac{5}{2}

化简

tan (x) = \frac{5}{2}

tan (x) = \frac{5}{2}

使用反三角函数性质

tan (x) = \frac{5}{2}

tan (x) = \frac{5}{2}

的通解

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

x = arctan (\frac{5}{2}) + 18 0^{\circ} n

x = arctan (\frac{5}{2}) + 18 0^{\circ} n

在

0 \leq x < 36 0^{\circ}

范围内的解

x = arctan (\frac{5}{2}), x = arctan (\frac{5}{2}) + 18 0^{\circ}

以小数形式表示解

x = 1.19028 \dots, x = 1.19028 \dots + 18 0^{\circ}

作图

流行的例子

cos(x)=(1-2)/(sqrt(26))

cos (x) = \frac{1 - 2}{26}

4cos(2x)-2sin(2x)=0

4 cos (2 x) - 2 sin (2 x) = 0

cos(2x)sin(x)+sin(x)=5cos(2x)+5

cos (2 x) sin (x) + sin (x) = 5 cos (2 x) + 5

sec(x)=1,-2pi<= x<= 2pi

sec (x) = 1, - 2 π \leq x \leq 2 π

tan(t)= 4/3 ,sin(t)

tan (t) = \frac{4}{3}, sin (t)