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受欢迎的三角函数 >

2tan^2(300)+3sin^2(150)-cos^2(180)

解答

2 tan^{2} (30 0^{\circ}) + 3 sin^{2} (15 0^{\circ}) - cos^{2} (18 0^{\circ})

解答

\frac{23}{4}

+1

十进制

5.75

求解步骤

2 tan^{2} (30 0^{\circ}) + 3 sin^{2} (15 0^{\circ}) - cos^{2} (18 0^{\circ})

tan (30 0^{\circ}) = tan (12 0^{\circ})

tan (30 0^{\circ})

将

30 0^{\circ}

改写为

18 0^{\circ} + 12 0^{\circ}

= tan (18 0^{\circ} + 12 0^{\circ})

使用周期

tan

:

tan (x + 18 0^{\circ}) = tan (x)

tan (18 0^{\circ} + 12 0^{\circ}) = tan (12 0^{\circ})

= tan (12 0^{\circ})

= 2 tan^{2} (12 0^{\circ}) + 3 sin^{2} (15 0^{\circ}) - cos^{2} (18 0^{\circ})

使用三角恒等式改写:

tan^{2} (12 0^{\circ}) = sec^{2} (12 0^{\circ}) - 1

tan^{2} (12 0^{\circ})

使用毕达哥拉斯恒等式:

tan^{2} (x) + 1 = sec^{2} (x)

tan^{2} (x) = sec^{2} (x) - 1

= sec^{2} (12 0^{\circ}) - 1

= 2 (sec^{2} (12 0^{\circ}) - 1) + 3 sin^{2} (15 0^{\circ}) - cos^{2} (18 0^{\circ})

使用以下普通恒等式:

sec (12 0^{\circ}) = - 2

sec (12 0^{\circ})

sec (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= - 2

使用以下普通恒等式:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\circ})

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

使用以下普通恒等式:

cos (18 0^{\circ}) = (- 1)

cos (18 0^{\circ})

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= 2 ((- 2)^{2} - 1) + 3 (\frac{1}{2})^{2} - (- 1)^{2}

化简

2 ((- 2)^{2} - 1) + 3 (\frac{1}{2})^{2} - (- 1)^{2} : \frac{23}{4}

2 ((- 2)^{2} - 1) + 3 (\frac{1}{2})^{2} - (- 1)^{2}

2 ((- 2)^{2} - 1) = 6

2 ((- 2)^{2} - 1)

(- 2)^{2} = 4

(- 2)^{2}

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 2)^{2} = 2^{2}

= 2^{2}

2^{2} = 4

= 4

= 2 (4 - 1)

数字相减:

4 - 1 = 3

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

3 (\frac{1}{2})^{2} = \frac{3}{4}

3 (\frac{1}{2})^{2}

(\frac{1}{2})^{2} = \frac{1}{2 ^{2}}

(\frac{1}{2})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

使用法则

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

= 3 \cdot \frac{1}{2 ^{2}}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 3}{2 ^{2}}

数字相乘:

1 \cdot 3 = 3

= \frac{3}{2 ^{2}}

2^{2} = 4

= \frac{3}{4}

(- 1)^{2} = 1

(- 1)^{2}

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 1)^{2} = 1^{2}

= 1^{2}

使用法则

1^{a} = 1

= 1

= 6 + \frac{3}{4} - 1

数字相减:

6 - 1 = 5

= \frac{3}{4} + 5

将项转换为分式:

5 = \frac{5 \cdot 4}{4}

= \frac{5 \cdot 4}{4} + \frac{3}{4}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{5 \cdot 4 + 3}{4}

5 \cdot 4 + 3 = 23

5 \cdot 4 + 3

数字相乘:

5 \cdot 4 = 20

= 20 + 3

数字相加:

20 + 3 = 23

= 23

= \frac{23}{4}

= \frac{23}{4}

流行的例子

cos(2x)=-(sqrt(3))/2 ,-pi<= x<= pi/2

cos (2 x) = - \frac{3}{2}, - π \leq x \leq \frac{π}{2}

cos(2θ)=cos^2(θ)-1/2

cos (2 θ) = cos^{2} (θ) - \frac{1}{2}

arccos(cos((7pi)/6))

arccos (cos (\frac{7 π}{6}))

cos (6 0^{\circ})

sin^{2} (2 x) = 1