sin(θ)=(7sin(140))/(16.12288984)

解答

sin (θ) = \frac{7 sin ( 14 0 ^{\circ} )}{16.12288984}

θ = 0.28283 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.28283 \dots + 36 0^{\circ} n

弧度

θ = 0.28283 \dots + 2 πn, θ = π - 0.28283 \dots + 2 πn

求解步骤

sin (θ) = \frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}

使用反三角函数性质

sin (θ) = \frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}

sin (θ) = \frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}

的通解

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

θ = arcsin (\frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}) + 36 0^{\circ} n

θ = arcsin (\frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{7 sin ( 14 0 ^{\circ} )}{16.12288 \dots}) + 36 0^{\circ} n

以小数形式表示解

θ = 0.28283 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.28283 \dots + 36 0^{\circ} n

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

tan (2 x) + sec (2 x) = 5

tan (2 x) + sec (2 x) = 1

cos^{2} (x) = \frac{( 4 k - 5 )}{10}

csc (A) = 3