(a) Show that for a projectile the angle between the velocity and the x - axis as a function of time is given by
`theta(t)="tan"^(-1)((v_(0y)-"gt")/(v_(@)x))`
(b) Shows that the projection angle `theta_(@)` for a projectile launched from the origin given by
`theta_(0)=tan^(-1)((4h_(m))/(R))`
where the symbols have their usual meaning.

The acute angle between the line 3x-4y=5 and the circle x^2+y^2-4x+2y-4=0 is theta . Then 9costheta=

theta is acute angle between the lines x^(2)-xy-6y^(2)=0 , then (2costheta+3sintheta)/(4sintheta+5costheta) is

Show that the function f given by f(x) = tan^(-1) (sin x+cosx ) , x gt 0 is always an increasing function in (0,(pi)/(4)) .

Find the angle between the tangents drawn from the origin to the parabolas y^2=4a(x−a) (a) 90^@ (b) 30^@ (c) tan^-1 (1/2) (d) 45^@

Find the dimensional formulae of the following quantities: a. the universal constant of gravitation G, b. the surface tension S, c. the thermal conductivity k and d. the coeficient of viscosity eta . Some equation involving these quantities are F=(Gm_1m_2)/r^2, S= (rho g r h)/2, Q=k(A(theta_2-theta_1)t)/d and F=- eta A (v_2-v_1)/(x_2-x_1) where the symbols have their usual meanings.

The angle between the pair of straight lines y^(2)sin^(2)theta - xy sin^(2)theta+ x^(2)(cos^(2)theta - 1) = 0 is

The angle between the tangents to the curves y=x^2a n dx=y^2a t(1,1) is cos^(-1)(4/5) (b) sin^(-1)(3/5) tan^(-1)(3/4) (d) tan^(-1)(1/3)

The angle between the lines joining origin to the points of intersection of the line sqrt(3)x+y=2 and the curve y^2-x^2=4 is (A) tan^(-1)(2/(sqrt(3))) (B) pi/6 (C) tan^(-1)((sqrt(3))/2) (D) pi/2

Prove that the angle between the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve x^2+2x y+3y^2+4x+8y-11=0 is tan^(-1)((2sqrt(2))/3)