sec 2 θ = 1 + tan 2 θ {\displaystyle \sec ^{2}\theta =1+\tan ^{2}\theta }
0 = tan θ Δ x − Δ y + 4.9 ( Δ x v cos θ ) 2 {\displaystyle 0=\tan \theta \Delta x-\Delta y+4.9\left({\frac {\Delta x}{v\cos \theta }}\right)^{2}}
0 = tan θ Δ x − Δ y + 4.9 ( 1 + tan 2 θ ) ( Δ x v ) 2 {\displaystyle 0=\tan \theta \Delta x-\Delta y+4.9(1+\tan ^{2}\theta )\left({\frac {\Delta x}{v}}\right)^{2}}
tan θ = Δ x ± Δ x 2 − 96.04 ( Δ x v ) 2 ( ( Δ x v ) 2 − Δ y ) 9.8 ( Δ x v ) 2 {\displaystyle \tan \theta ={\frac {\Delta x\pm {\sqrt {\Delta x^{2}-96.04\left({\frac {\Delta x}{v}}\right)^{2}(\left({\frac {\Delta x}{v}}\right)^{2}-\Delta y)}}}{9.8\left({\frac {\Delta x}{v}}\right)^{2}}}}
tan θ = Δ x ± Δ x 1 − 96.04 ( 1 v ) 2 ( ( Δ x v ) 2 − Δ y ) 9.8 ( Δ x v ) 2 {\displaystyle \tan \theta ={\frac {\Delta x\pm \Delta x{\sqrt {1-96.04\left({\frac {1}{v}}\right)^{2}(\left({\frac {\Delta x}{v}}\right)^{2}-\Delta y)}}}{9.8\left({\frac {\Delta x}{v}}\right)^{2}}}}
tan θ = v 2 1 ± 1 − 96.04 ( 1 v ) 2 ( ( Δ x v ) 2 − Δ y ) 9.8 Δ x {\displaystyle \tan \theta =v^{2}{\frac {1\pm {\sqrt {1-96.04\left({\frac {1}{v}}\right)^{2}(\left({\frac {\Delta x}{v}}\right)^{2}-\Delta y)}}}{9.8\Delta x}}}
θ = arctan ( v 2 1 ± 1 − 96.04 ( 1 v ) 2 ( ( Δ x v ) 2 − Δ y ) 9.8 Δ x ) {\displaystyle \theta =\arctan \left(v^{2}{\frac {1\pm {\sqrt {1-96.04\left({\frac {1}{v}}\right)^{2}(\left({\frac {\Delta x}{v}}\right)^{2}-\Delta y)}}}{9.8\Delta x}}\right)}
