Purchase Solution

Trigonometric constants

Not what you're looking for?

Ask Custom Question

1) Express (cosx)^n in terms of sums of coskx
2) Express (sinx)^n in terms of sums of coskx or sinkx
3) Express cosnx in terms of sums of (cosx)^k
4) Express sinnx in terms of sums of (sinx)^k
5) Derive exact trigonometric identities for sin(k*pi) for k being:
1/12, 1/10,1/8,1/6,1/5,1/4,3/10,1/3,3/8,2/5,5/12

Attachments
Purchase this Solution
Solution Summary

This provides several examples of working with exact trigonometric constants. The expert derives the exact trigonometric identities for the functions.

Solution Preview

Please see attached

Powers of Sine and Cosine

1) It can be useful to express in terms of sums of :
First for even powers:

Conclude
Or

There is a corollary from this, integrating the left hand side is a lot harder than integrating the left hand side:

Conclude

2) Now for odd powers:

Conclude
Or

There is a corollary from this, integrating the left hand side is a lot harder than integrating the left hand side:

Conclude ...

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Verifying Trigonometric Identities

    Hence the general solution of the recurrence relation is given by Where are arbitrary constants. Expressing the solution can be rewritten as Trigonometric identities are verified. The solution is detailed and well presented.

  • ODE - Method of Variation of Coefficients

    Sine trigonometric functions are solved.

  • Initial value problem

    Thus we can use the method of undetermined coefficient, in which we "guess" a solution in the form of the non homogenous term and solve for the unknown constants.

  • Circuit analysis - Differential Equation

    We have: with L and R being constants. There are good references which relate to solving these equations.

  • improper rational function

    The constants on the tops of both of these fractions can be taken outside of the integrals and simple u substitutions will give you the solution . 10. Evaluate: This problem can be solved with a trigonometric substitution letting with .

  • Calculus of variations functions

    cosh(x), the solution (17) of ODE (15) reads: ( 32) and replacing C1 and C2 with (31), the final form of solution will be: ( 33) and, by applying one of the properties of trigonometric

  • Laplace equation in cylindrical coordinates

    However, Thus the radial solution is: Combining it all we obtain the general solution for the potential: Where all the integration constants were lumped together Now, for the boundary conditions: Since we require the function

  • Trigonometry - Easy method to learn and memorize identities

    4021 Trigonometric Functions and Trigonometric Identities I need to know the trigonometric functions and trigonometric identities. Please see the attached file. The primary use of trigonometric functions is in the measurement of angles.

  • Two sound waves are emitted; show equation of the sum and beat frequency of waves

    7546 Two sound waves are emitted; show equation of the sum Two sound waves are emitted: y1, with frequency f1, and y2, with frequency f2, with other constants identical, as expressed below.

View More Related Solutions