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受欢迎的三角函数 >

sin(x)+cos(x)= 3/2

解答

sin (x) + cos (x) = \frac{3}{2}

解答

x \in R 无解

求解步骤

sin (x) + cos (x) = \frac{3}{2}

使用三角恒等式改写

sin (x) + cos (x)

sin (x) + cos (x) = 2 sin (x + \frac{π}{4})

sin (x) + cos (x)

改写为

= 2 (\frac{1}{2} sin (x) + \frac{1}{2} cos (x))

使用以下普通恒等式:

cos (\frac{π}{4}) = \frac{1}{2}

使用以下普通恒等式:

sin (\frac{π}{4}) = \frac{1}{2}

= 2 (cos (\frac{π}{4}) sin (x) + sin (\frac{π}{4}) cos (x))

使用角和恒等式:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= 2 sin (x + \frac{π}{4})

= 2 sin (x + \frac{π}{4})

2 sin (x + \frac{π}{4}) = \frac{3}{2}

两边除以

2

2 sin (x + \frac{π}{4}) = \frac{3}{2}

两边除以

2

\frac{2 sin ( x + \frac{π}{4} )}{2} = \frac{\frac{3}{2}}{2}

化简

\frac{2 sin ( x + \frac{π}{4} )}{2} = \frac{\frac{3}{2}}{2}

化简

\frac{2 sin ( x + \frac{π}{4} )}{2} : sin (x + \frac{π}{4})

\frac{2 sin ( x + \frac{π}{4} )}{2}

约分:

2

= sin (x + \frac{π}{4})

化简

\frac{\frac{3}{2}}{2} : \frac{3 2}{4}

\frac{\frac{3}{2}}{2}

使用分式法则:

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

= \frac{3}{2 2}

\frac{3}{2 2}

有理化:

\frac{3 2}{4}

\frac{3}{2 2}

乘以共轭根式

\frac{2}{2}

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

222 = 4

222

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

222 = 2 \cdot 2^{\frac{1}{2}} \cdot 2^{\frac{1}{2}} = 2^{1 + \frac{1}{2} + \frac{1}{2}}

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

同类项相加:

\frac{1}{2} + \frac{1}{2} = 2 \cdot \frac{1}{2}

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

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

2 \cdot \frac{1}{2}

分式相乘:

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

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

约分:

2

= 1

= 2^{1 + 1}

数字相加:

1 + 1 = 2

= 2^{2}

2^{2} = 4

= 4

= \frac{3 2}{4}

= \frac{3 2}{4}

sin (x + \frac{π}{4}) = \frac{3 2}{4}

sin (x + \frac{π}{4}) = \frac{3 2}{4}

sin (x + \frac{π}{4}) = \frac{3 2}{4}

- 1 \leq sin (x) \leq 1

x \in R 无解

作图

流行的例子

cos^2(x)-sin^2(x)-5sin(x)=3

cos^{2} (x) - sin^{2} (x) - 5 sin (x) = 3

sin(θ)=-(sqrt(21))/5

sin (θ) = - \frac{21}{5}

solvefor t,cos(2t)-sin(t)=sqrt(o)

so l v e f or t, cos (2 t) - sin (t) = o

cot (x) = - \frac{15}{8}

tan (x^{\circ}) = \frac{30}{73}