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受欢迎的三角函数 >

solvefor t,x=3cos(t)

解答

求解

t, x = 3 cos (t)

解答

t = arccos (\frac{x}{3}) + 2 πn, t = - arccos (\frac{x}{3}) + 2 πn

求解步骤

x = 3 cos (t)

交换两边

3 cos (t) = x

两边除以

3

3 cos (t) = x

两边除以

3

\frac{3 cos ( t )}{3} = \frac{x}{3}

化简

cos (t) = \frac{x}{3}

cos (t) = \frac{x}{3}

使用反三角函数性质

cos (t) = \frac{x}{3}

cos (t) = \frac{x}{3}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

t = arccos (\frac{x}{3}) + 2 πn, t = - arccos (\frac{x}{3}) + 2 πn

t = arccos (\frac{x}{3}) + 2 πn, t = - arccos (\frac{x}{3}) + 2 πn

作图

流行的例子

tan^2(θ)=-3/2 sec(θ),0<= θ<2pi

tan^{2} (θ) = - \frac{3}{2} sec (θ), 0 \leq θ < 2 π

5sin(x)+3cos(x)=0

5 sin (x) + 3 cos (x) = 0

sqrt(3)cos(x)csc(x)=2cos(x)

3 cos (x) csc (x) = 2 cos (x)

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

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

sin(x)=0,0<= x<2pi

sin (x) = 0, 0 \leq x < 2 π