Trigonometry

1) A security car with its spotlight on is parked 40 meters from a warehouse. Consider θ and x as shown in the figure. Write θ as a function of x.

2) A weight is oscillating on the end of a spring (see figure). The position of the weight relative to the point of equilibrium is given by   where y is the displacement(in meters) and t is the time (in seconds). Find the time when the weight is at the point of equilibrium (y = 0) for 0 ≤ t ≤ 1.

3) The horizontal distance d (in feet) traveled by a projectile with an initial speed of v feet per second is modeled by: 

where θ is the angle at which the projectile is launched.

Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 100 feet per second when the ball is hit at an angle of θ = 40°. Round to the nearest foot