Calculus help: properties of the trigonometric functions, range, maximum height, etc

[ihatemath0101]

Calculus help: properties of the trigonometric functions, range, maximum height, etc

(2) Pretend that Angry Birds are real. The path of an Angry Bird fired at an inclination $\displaystyle \theta$ to the horizontal with initial speed $\displaystyle v_0$ is a parabola. The range of the Angry Bird (the horizontal distance that it travels) is given by:

. . .$\displaystyle R\left(\theta,\, v_0\right)\, =\, \dfrac{v_0^2\, \sin\left(2\theta\right)}{g}$

...where $\displaystyle g\, \approx\, 9.8\, m/s^2$ is the acceleration due to gravity. The maximum height attained by the Angry Bird is given by:

. . .$\displaystyle H\left(\theta,\, v_0\right)\, =\,\dfrac{v_0^2\, \sin^2\left(\theta\right)}{2g}$

Find the range and maximum height of an Angry Bird fired at an angle 30° with an initial speed 200 m/s.

(3) Use properties of the trigonometric functions to find (without a calculator) the exact value of:

. . .$\displaystyle \sin\left(-\dfrac{\pi}{12}\right)\, \csc\left(\dfrac{25\pi}{12}\right)$

(4) The voltage $\displaystyle V$, in volts, produced by an AC generator at time $\displaystyle t$, in seconds, is $\displaystyle V(t)\, =\, 220\, \sin(120\pi t).$

(a) Graph $\displaystyle V$ over two periods, beginning at $\displaystyle t\, =\, 0$.

(b) If a resistance of $\displaystyle R\, =\, 10$ ohms is present, what is the current $\displaystyle I$? (Use Ohm's Law: $\displaystyle V\, =\, IR$)

(c) What is the amplitude and period of the current $\displaystyle I$?

(d) Graph $\displaystyle I$ over two periods, beginning at $\displaystyle t\, =\, 0$.

 

[Steven G]

Calculus help: properties of the trigonometric functions, range, maximum height, etc

For number 2 you are given the formula and the values to put into the formula. So what is the problem you are having? This is a very basic algebra problem which is called evaluate problems. Calculus demands you to have a very good understanding of algebra. If you do not you will not survive calculus. This is your education so maybe you should go back and restudy algebra so you can do well in calculus.

 

[Steven G]

Calculus help: properties of the trigonometric functions, range, maximum height, etc

The other two problems are standard trig problems. Did you take trigonometry? What results did you get when you tried these problems. We will show you your errors or the next step if you show us your work. If you can't even get started we will start you off but you need to let us know what is going on. Just remember that in the end you can do this!