# Question: Mathematical approximations

In physics it is important to use mathematical approximations. Demonstrate that for small angles (<20°) tan a ≈ sin a ≈ a = πa` /180°
Where, is in radians and a` is in degrees. Use a calculator to find the largest angle for which tan, may be approximated by sin, if the error is to be less than 10.0%.

## Answer to relevant Questions

A high fountain of water is located at the center of a circular pool as in Figure P1.61. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 15.0 m. Next, the student stands ...One cubic centimeter of water has a mass of 1.00 x 10-3 kg. (a) Determine the mass of 1.00 m3 of water. (b) Biological substances are 98% water. Assume that they have the same density as water to estimate the masses of a ...A particle moves according to the equation x = 10 t 2 where x is in meters and t is in seconds (a) Find the average velocity for the time interval from 2.00 to 3.00 s. (b) Find the average velocity for the time interval ...A 50.0-g superb all traveling at 25.0 m/s bounces off a brick wall and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the magnitude of the average ...A truck covers 40.0 m in 8.50 s while smoothly slowing down to a final speed of 2.80 m/s. (a) Find its original speed. (b) Find its acceleration.Post your question