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Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- Sketch the curve represented by each set of equations by eliminating the parameter. a. x=5cos and y=3sin,02 b. x=1+tan and y=2+2sec,/23/2arrow_forwardShooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the path of a projectile with initial speed v0=32ft/s, fired into a headwind of =24ft/s, for the angles =5,15,30,40,45,55,60 and 75. Is it still true that the greatest range is attained when firing at 45 ? Draw some more graphs for different angles, and use these graphs to estimate the optimal firing angle.arrow_forwardA golf ball is hit with an initial velocity of 135 feet per second (about 92 miles per hour) at an angle of 60 degrees to the horizontal. There is a 5 foot-per-second headwind that reduced the horizontal velocity by that amount. The vertical component of velocity is unaffected. Find parametric equations for the position of the ball relative to the tee as a function of time after it is hit. I= 135 cos 60π 180 5 =(1 y=-16t² + 135 sin 60π 180 After how many seconds does the ball hit the ground? t seconds How far does the ball travel before hitting the ground? feetarrow_forward
- 1. please solve it on paperarrow_forwardFind the Cartesian equation of the image of the line x = 2 under the mappingz → sin(z). Sketch the image. If the pre-image point move on x = 3 from bottom to top, what is the orientation of the image point?arrow_forwardSketch the parametric curve for each pair of parametric equations. Use arrows to show the orientation of the curve corresponding to increasing values of t. Use a table and substitution to solve.arrow_forward
- Which graph is the one described by the set of parametric equations, (x = t for - 00arrow_forwardSuppose the parametric equations for a moving charged particle in an electromagnetic field take the following forms: The trajectory of such a moving particle is shown in the figure below, where 0 ≤ts Find the length of arc ABC. Note: cos(21) = 1 - 2sin² (t), cos(a - B) = cos(a) cos(B) + sin(a) sin(B). · · Position y in meters 15 10 x = 11 · cos(t) — 6 · cos, y = 11 · sin(t) — 6 · sin -5 -10 -20 -15 B -10 -5 0 Position x in meters 5 10 Figure 1: Trajectory of a particle for 0 ≤ t ≤arrow_forward1. Find the equation for the tangent line for the following parametric equation, do not change to Cartesian coordinates. Show all of your work. Write your answer as exact answers. x = t² – 6, y = t³ + t,t = -1arrow_forwardRecommended textbooks for you
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