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受欢迎的三角函数 >

5tan^2(A)-7=8

解答

5 tan^{2} (A) - 7 = 8

解答

A = \frac{π}{3} + πn, A = \frac{2 π}{3} + πn

+1

度数

A = 6 0^{\circ} + 18 0^{\circ} n, A = 12 0^{\circ} + 18 0^{\circ} n

求解步骤

5 tan^{2} (A) - 7 = 8

用替代法求解

5 tan^{2} (A) - 7 = 8

令

: tan (A) = u

5 u^{2} - 7 = 8

5 u^{2} - 7 = 8 : u = 3, u = - 3

5 u^{2} - 7 = 8

将

7

到右边

5 u^{2} - 7 = 8

两边加上

7

5 u^{2} - 7 + 7 = 8 + 7

化简

5 u^{2} = 15

5 u^{2} = 15

两边除以

5

5 u^{2} = 15

两边除以

5

\frac{5 u ^{2}}{5} = \frac{15}{5}

化简

u^{2} = 3

u^{2} = 3

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = 3, u = - 3

u = tan (A)

代回

tan (A) = 3, tan (A) = - 3

tan (A) = 3, tan (A) = - 3

tan (A) = 3 : A = \frac{π}{3} + πn

tan (A) = 3

tan (A) = 3

的通解

tan (x)

周期表（周期为

πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

A = \frac{π}{3} + πn

A = \frac{π}{3} + πn

tan (A) = - 3 : A = \frac{2 π}{3} + πn

tan (A) = - 3

tan (A) = - 3

的通解

tan (x)

周期表（周期为

πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

A = \frac{2 π}{3} + πn

A = \frac{2 π}{3} + πn

合并所有解

A = \frac{π}{3} + πn, A = \frac{2 π}{3} + πn

作图

流行的例子

tan (x) = \frac{28}{16}

2sin^2(x)=3-sin(x)

2 sin^{2} (x) = 3 - sin (x)

9tan(2x)-18cos(x)=0

9 tan (2 x) - 18 cos (x) = 0

8cos(2t)-14sin(2t)=0

8 cos (2 t) - 14 sin (2 t) = 0

1-sqrt(2)sin(θ)=0

1 - 2 sin (θ) = 0