Trigonometry is involved in many fields of physics. oscillations, waves and optics are the most common of them. Deep at essential knowledge of trigonometric functions and equations is very important. And I'm trying to help you go through this part of math step by step, we have to start with units of angles, radians and degrees. Typically, life is based mainly on using degrees. But working on physics problems.
Radians are strongly recommended, if not necessarily, conversions from radians to degrees, and vice versa, are common and easy. Just take a look at these formulas, which can give you the unit you need for any specific application you're working on. The second tool a student must use is the trigonometric circle, extremely powerful to anyone who needs to solve a problem really fast and Easy trigonometric functions and equations are last but not least, I will try to highlight the way of using them in physics through the following example. A small object undergoes a simple harmonic motion having velocity given by the equation, V equals point two times sine of two times pi times three, plus pi over four. Determine the time needed to reach its maximum positive value for first time. After t equals zero.
As you can see, we have to use the given equation of velocity and substitute its maximum value on it. Doing this a trigonometric equation is produced, which can easily be solved through T. Pay attention at the appropriate use of values of constant key, which in this case must be put equal to zero. Since we need to find the time when the velocity is Maximum for the first time. Okay, first time after t zero. If we had found a not acceptable value of t, for example, and negative one, then t equals one would give us the correct answer. Finally, I do believe that is useful to know that trigonometric identities are important when someone is involved in problems of oscillations and waves.
That's why I have written the most common use of this slide. Another characteristic example is necessary again, is stone is launched at various angles about horizontal having an initial velocity. Prove that the maximum horizontal distance, in other words range will be maximized for angle of 45 degrees. The main concept has to do with the equation of vertical displacement during a project Motion. When the object reaches the axis x after it is launched, the instantaneous magnitude of y is zero. putting it on this equation gives us a quadratic equation for time t. The accepted solution of time can be substituted on the equation of horizontal displacement x.
As you can see, now, the term two times sine theta times cosine theta can be written in an equivalent for us, sine of two times theta, which would obviously be maximized if two times theta equals 90 degrees, or theta equals 45 degrees. That's all really interesting and easy. All you need is to practice a little more. Thank you again.