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受欢迎的三角函数 >

-3sin(t)+4cos(t)=0

解答

- 3 sin (t) + 4 cos (t) = 0

解答

t = 0.92729 \dots + πn

+1

度数

t = 53.13010 \dots^{\circ} + 18 0^{\circ} n

求解步骤

- 3 sin (t) + 4 cos (t) = 0

使用三角恒等式改写

- 3 sin (t) + 4 cos (t) = 0

在两边除以

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

\frac{- 3 sin ( t ) + 4 cos ( t )}{cos ( t )} = \frac{0}{cos ( t )}

化简

- \frac{3 sin ( t )}{cos ( t )} + 4 = 0

使用基本三角恒等式:

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

- 3 tan (t) + 4 = 0

- 3 tan (t) + 4 = 0

将

4

到右边

- 3 tan (t) + 4 = 0

两边减去

4

- 3 tan (t) + 4 - 4 = 0 - 4

化简

- 3 tan (t) = - 4

- 3 tan (t) = - 4

两边除以

- 3

- 3 tan (t) = - 4

两边除以

- 3

\frac{- 3 tan ( t )}{- 3} = \frac{- 4}{- 3}

化简

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

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

使用反三角函数性质

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

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

的通解

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

t = arctan (\frac{4}{3}) + πn

t = arctan (\frac{4}{3}) + πn

以小数形式表示解

t = 0.92729 \dots + πn

作图

流行的例子

cos (θ) = \frac{8}{6}

tan(x)=(-2sqrt(2))/2

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

arctan(0.1x)+arctan(0.01x)=39

arctan (0.1 x) + arctan (0.01 x) = 3 9^{\circ}

1 = tan (t)

sin(c)=(5sin(140))/7

sin (c) = \frac{5 sin ( 14 0 ^{\circ} )}{7}