In physics it is important to use mathematical approximation

In physics, it is important to use mathematical approximations. For small enough angles,

tan() sin()

where is in radians. (How small \"small enough\" is depends on the level of accuracy you need....)

Use a calculator or computer to find the largest whole number of degrees for which sin() may be approximated by if the error is to be less than 1.0%.

Solution

sin(8⁰) = 0.139173

tan(8⁰) = 0.14054

tan(8⁰) - sin(8⁰) = 0.001367

error % = [tan(8⁰) - sin(8⁰) / sin(8⁰)] x 100

= (0.001367/ 0.139173) x 100

= 0.98 %

< 1 %

Hence,

= 8⁰

Therefore,

Required largest whole number of degrees = 8⁰