# Trigonometry in Physics

Demands of Trigonometry in Physics are enormous. So many problems in Physics can be solved only by Trigonometry. Mostly all section of Physics needs Trigonometry.

Especially in Rotational motion, Gravitation, Motion in a plane, Wave mechanics, Optics, Electric charges etc.Some application based on Trigonometry in PhysicsThere are many examples of Application of Trigonometry in Physics.Here we are stating some examples related to that.Calculation of Angular Momentum:Anything related to angle we use trigonometry.

Angular momentum is one of the examplesImage of Angular momentumImage of Angular momentumLet us consider a particle P of mass m, moving uniformly in a straight line S with a velocity v. Let the origin O, be a point outside the line Sand let us denote the position vector op by r. ON is the perpendicular from O to the line S and its length is given by ON="OPsin" ө. Ө is the angle between the position vector r and the velocity vector v.

The angular momentum L of the particle about the origin O is defined to be the product of ON with the momentum of the particle mv.L="m" v r sin өCalculation on gravitational motion:We use trigonometry in gravitational motion also. For calculating orbital speed of a geostationary satellite we have to use trigonometry.Example:To what latitude does the geostationary satellite coverage extend? What is the orbital speed of that?Solution:Image of EquatorImage of EquatorThe latitude of the coverage is λ. That we have to find out using basic Trigonometry.

From above figure we can see that the latitude of the coverage extends up to the tangent SP.From the right angled triangle OPS,we have ,cos λ = OP/OS = division of two numbersOP = radius of earth(radius of earth),OS = Distance of the satellite from the center of earth(Distance of the satellite from the center of earth)Thus λ = 81.3degree.A 9degree circular arc around the pole is left uncovered. So 3 satellites ae needed to cover the entire earth.The orbital speed of the satellite will be,V = 2πa/T= 2`xx` division of numbers= 3.07X102ms-1Conclusion for use of trigonometry in physicsWe have seen varied usage of trigonometry and its application to physics. Trigonometry was first applied in calculation related to Spherical bodies in Physics.Physical chemistry also need Trigonometry for different calculations.