解三角函數聯立到可按計算機?

- 5*sin θ = - v / √2 = 2 + 5*cos θ
sin θ = - 0.4 - cos θ
1 = sin²θ + cos²θ = ( - 0.4 - cos θ )² + cos²θ

令 x = cos θ
2x² + 0.8x - 0.84 = 0
x² + 0.4x - 0.42 = 0

x
= [ - 0.4 ± √( 0.4² + 4*0.42 ) ] / 2
= - 0.2 ± (1/2)√1.84
≒ - 0.878232998312527 , 0.478232998312527 , 此步驟開始要用到工程計算機
正值不合, 因為 x = cos θ , 且 θ 在第二象限.
因此, x = cos θ ≒ - 0.878232998312527

θ
= arccos ( - 0.878232998312527 )
≒ 2.64295104240389 rad
= ( 2.64295104240389 * 180 / π )°
≒ 151.43°

由 v / √2 = 5 * sin θ 可得 :

v
= 5√2 * sin θ
= 5√2 * sin 151.43°
≒ 3.38