find angle given point the trajcetory passes through and inital velocity

Question

I'm currently studying M1 for A level maths and we've derived the equation to prove that the trajectory is a parabola.

$y=x\tan\theta - \sec^2\theta \dfrac{gx^2}{2u^2}$

I am curious as to how to rearrange the equation to make $\theta$ the subject. I have tried myself and am unable to do so.

Any help?

Answer 1

Let the point of projection of projectile be (h,k) therefore it satisfies the equation of trajectory of the parabolic path of projectile. satisfying (h,k) we get k=htanθ-〖gh/(〖2u〗^2 cos⁡〖θ cos⁡θ 〗 )〗^2 By solving the equation in terms of tan we get the following equation 〖gh〗^2/u^2 +k=(2h tan⁡θ+k(〖〖tan〖^2〗〗⁡θ〗^ -1))/(1+〖tan〖^2〗〗⁡θ ) Thus the equation relates angle of projection with the point of projection and the equation of trajectory. Equation can be obtained by simple half angle identities and conversion of sine and cosine into tangent function