Applying small angle approximations for sin(x), cos(x) and tan(x) : ExamSolutions Maths Revision

[@pointlessvidios]

hadn't been taught any of this and yet had it for homework and no one knew what was going on aha, absolute life saver!!!

[@rangariraitakavingei6034]

i really got a btter view on this topic,Thank you soo much!!

[@ExamSolutions_Maths]

You're welcome.

[@sea5205]

This guy is the best

[@poinchesterstation4514]

what would 3cos3x be? would it be 3-27x^2 over 2

[@ExamSolutions_Maths]

Only if x were very small. Compare your answers on a calculator but make sure you are in radians.

[@jackpickford4918]

So say for example cos(x - y) where x and y are two different unrelated angles (ie arms of a pendulum system) would its small angle approximation be almost 1 or x - y?

[@ExamSolutions_Maths]

cos(x-y) expanded is cosx cos y - sin x sin y so using the small angle approximations this would be (1-x^2/2)(1-y^2/2) - xy

[@jackpickford4918]

ExamSolutions is it not Cos x cos y + sin x sin y?

[@ExamSolutions_Maths]

Oops! Yes you are correct. Quickly answered and careless mistake.

[@YH-cq5qf]

Hello,silly question but say we had a constant in the numerator and say sin(x) as the denominator and x was small,would the fraction just tend to infinity?Then would my answer be tending to or ~infinity

[@ExamSolutions_Maths]

Say you have a positive constant A in the numerator and x was a small positive angle then sin(x) tends to positive x which tends to zero. So A/x tends to a very large positive value. If x is a small negative value then sin(x) tends to a small negative value of x and so A/x tends to a large negative value. I hope that answers your question.

[@YH-cq5qf]

ExamSolutions I see,thanks for your reply.

[@NomanKhan-bd4st]

i love youu