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受欢迎的三角函数 >

1sin(30)=1.495sin(x)

解答

1 sin (3 0^{\circ}) = 1.495 sin (x)

解答

x = 0.34101 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.34101 \dots + 36 0^{\circ} n

+1

弧度

x = 0.34101 \dots + 2 πn, x = π - 0.34101 \dots + 2 πn

求解步骤

1 \cdot sin (3 0^{\circ}) = 1.495 sin (x)

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

使用以下普通恒等式:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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}

= \frac{1}{2}

1 \cdot \frac{1}{2} = 1.495 sin (x)

交换两边

1.495 sin (x) = 1 \cdot \frac{1}{2}

在两边乘以

1000

1.495 sin (x) = 1 \cdot \frac{1}{2}

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

1.495 sin (x) \cdot 1000 = 1 \cdot \frac{1}{2} \cdot 1000

整理后得

1495 sin (x) = 500

1495 sin (x) = 500

两边除以

1495

1495 sin (x) = 500

两边除以

1495

\frac{1495 sin ( x )}{1495} = \frac{500}{1495}

化简

sin (x) = \frac{100}{299}

sin (x) = \frac{100}{299}

使用反三角函数性质

sin (x) = \frac{100}{299}

sin (x) = \frac{100}{299}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{100}{299}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{100}{299}) + 36 0^{\circ} n

x = arcsin (\frac{100}{299}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{100}{299}) + 36 0^{\circ} n

以小数形式表示解

x = 0.34101 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.34101 \dots + 36 0^{\circ} n

作图

流行的例子

csc(θ)=-37/12 ,(3pi)/2 <= θ<= 2pi

csc (θ) = - \frac{37}{12}, \frac{3 π}{2} \leq θ \leq 2 π

7sin(2ϕ)+12cos(ϕ)=0

7 sin (2 ϕ) + 12 cos (ϕ) = 0

sec(θ/2)=cos(θ/2)

sec (\frac{θ}{2}) = cos (\frac{θ}{2})

2cos^2(x)-1.28=0

2 cos^{2} (x) - 1.28 = 0

cos^3(3θ)= 1/4

cos^{3} (3 θ) = \frac{1}{4}