With this Power Reducing Calculator you can learn and apply bunch of new things. You can bind specific formulas to the term power reduction. These are formulas for reducing power related to square trigonometric functions and the cosine of the doubled angle – cos (2x). It is a quick and straightforward transition method between the forces of trigonometric functions. Below, we will present how to use our power reducing calculator and more information about the necessary trigonometric functions and the rules you need to follow.

Meanwhile, use CalCon’s calculators to calculate the cofunction and learn how to find the value of the inverse sine (arcsin) or inverse cosine (arccos) value. Check our official website and learn new things!

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Power Reducing: Trigonometric Functions

Specifically, the term trigonometry had its roots in the 16th century. It was formed by combining the words trignon and metron, of Greek origin. In ancient times people used trigonometry to calculate the values ​​of unknown parts of a triangle or any other geometric shape that you could divide into triangles.

Accordingly, trigonometry is the branch of math that deals with the special functions of angles and their relations. Specifically, there are six different angle functions that you can use in trigonometry.

These are the sine function (sin), the cosine function (cos), the tangent function (tan), the cotangent function (cot), the secant function (sec) and the cosecant function (csc). All functions are a property of an angle depending on the shape and type of the torus. On the whole, you can use them to calculate the value of unknown angles. 

This branch of math arose exclusively due to the need to calculate values ​​in astronomy and special geodetic research. In fact, all the problems that required answers were related to the relationship between angles and distances in three-dimensional space.

You can also use these six functions with Pythagorean identity. To use these values in practice, they need to be accessible from any angle. Furthermore, you can easily find function values ​​for all angles from 0 to 45 degrees.

Power Reducing Identities/formulas

The type of trigonometric identities reduces power identities. These power reducing identities have their formulas to prove their identity. They can help find the values of complex trigonometric functions and equations. When calculating square, cubes, fourth, fifth trigonometric functions, you can mainly use these power reducing identities.

Power reducing identities lead you to increase your way of manually calculating certain complex trigonometric equations. Each identity has its appropriate formula that you can combine to solve a particular task. You can report identities using the double-angle and half-angle formulas.

In the following table, you can see basic formulas that you need to prove the power reducing identities: 

FunctionPower-reducing FormulaDouble angle FormulaHalf angle Formula
SINJW7KUhRVpYX64OGeHwd0v dOlNM7yjMd 8YWlGRe1 WlbEC8fMFUnDdCF3ghxC2F0qOIzHWkEAmWfnbZL4FRdjJ6JXYjwiPMWFEMQwngFvhaMzBRBEJyGLNY XjaF2DCfCHrC6ps9 wscQaLaSPfNRhF8ti8kK8kE2i6uuB8FQor7vvaXi3YWCUln4Y93RuoXJPDogHhoFi1OdIoyVvgA0Cycs4BzI4UIev4zDneE6zsX90R5ihCfnHAL9 hnp5GF2J792dnv4KNVXvdVzvLiPKHYvaRIDRjhpjcCCqQZW3psQMj s5f45NU1HB76Ktcr
COS87b uG Demtnp1 1dNgpQ2fsH5pfD8MghFsNfS8NRb4wOWfydxQQKwq jiDW6x2r0Gw2ZQ92kE3JUoANrCxnS2eqO6 RLWVxEYUYyNY65BxfrzeYCmkdhhORVbZnOlDU15KVjx8SBZRpZPBOFRUK oR9uBeawCLM5h5ivD zBRDK9HwI 62ytVKFG45IwJ5 P7zjR8 nJicEpcu
TANZsM1Rb6uJmR7t0fqhGMdcqN8KoUS5yrcObImpNh fBWRajrL3JZ9dfVIoE2pheGMD0xH 0OpkfB7XBJMeHalRPDHe3MaLDGC5TuizqfM PMKJWJGubDvH0CkW54y5m74RhfN9P5apfF8Zko4O8wga loagrJQT yA7S5B1iOxUr1PW2rNXyqGEz4nbJGhOjm0wzId8yd3cOP53tNd5EhFHGm7Q MSZT67QV ThEEW9RKl3DJiollcPDZQj2V6yN1BzK9QaA0kHGmKCov
Formulas for power-reducing identities

The next simple example can explain to you the purpose of using reducing power identities and formulas. Suppose you need to find the value of sin (4x). If you want to simplify, you can write the expression applying powers up to one. So it will look like this:

\sin^{4}x = (\sin^{2}x)^{2}=\left (\frac{1-\cos2x}{2} \right)^{2} = \frac{1-2 \cos2x+\cos^{2}x}{2}

Power Reduction Rule

The purpose of using power reducing rules is to record a trigonometric expression without exponents. You can use these rules, identities, and formulas for more straightforward calculations by deriving the known formulas for double angle, half-angle, and Pythagorean identity. You can also use formulas to calculate angles by solving exponents of trigonometric function.

Power-reducing Formula – sine function (sin)Power-reducing Formula – cosine function (cos)Pythagorean identity
SquaresUjjhyRurGMNK3ViR dkZWH8GaOo bnXgsqOafgn0Ap6 xAmAX3Q3ZuNePniLLhS aQiiDpExVvTN MezkHr3eCgdPTNooDG9L6i8Oro8QCnZLgijzecYJtGVwlvnBCVvDlNSfaMxc6ENQSmr3259QX7qhx7R tAZCulWptrBNy6quzpSY
CubesBZp9GL7j1TU Yt gTj6V2zCjZR9i99qFv9Xt2cAEN5gzc EMlXCOr3y5haumyOV4e0k7KMYXm1PDPw TTjq0bTRx32fa0ojsR2N3i5XIYALzv4hfE4WKZ0ABr0NUQF8eVC sBuKqXP3ovpMWNocIxBIpS97kFEk23zVVo3bVo9JyRE73drPffyiEhqzQ0PqsatE9GRL4GfxdrKFv6R JwDkp20o2U1 X3JQEwolmh5zNnOf F3AA5ovLLnU86yyQJBzWi0But3fbrYgH6U3WSfG0hU0NN5vbK8RNoYoPQJOwrbRrS i0sZVGnWUdF3uZgsoQrzP3znHR bKz8 qhON4t80umf0A68gzGE3rXVHJ9tRvA
FourthKWOzM5n1MXLgqYoeT5ufnX6kGUdY6mZiioEOi FoS8hjFKhaXsfHkWH3NdMZPLLSZ1qooqZn70H8ZHFe5VUI6v5LhNEBZwt4mg75NjlJnkgLBQdPoRzmBjIRNnbvK2KwYtmu8bDPbXcJuRrBaJlwtTzJT wQYF777gHInXY2ESOuNQW7iTLvQKahCefWqZoOTCuKA6ja4uJHcA7GUddBms59k91vNqgO wENnaZVWBp ZeD2pUcLrkYHgz0Oc0mOu4tr8gPf8dkzg6T5
FifthryLWYJdFeR8M5xsaxnCZC7L2x8nbd O28pP6v1 pZ AomVFivWYHF JxKPP yMRSI8kXhq sU4lk2mD8M tqj411OlWrmF4DGkIoa4xrkMxiZu2ZzLjrQaE iTrkfe mhAtXmtyxnaAfDP6lQuBsiU7v Q5IsQtKW63j4UiL7 YpYCgKow4p2TzzjXnEdGEYlaAGraLJDdrw OmOM4qcSW1hNxAQIz Yf7ZdeqpxN9nlSeq
Pythagorean identity vs power-reducing formula

Power Reducing Calculator – How to Use?

You can use our calculator in two ways. First of all, it is important to note that this calculator, like many others available on our official website, offers a fast way to calculate the desired value. In this case, we are solving trigonometric expressions and functions, reducing them to expressions without exponents.

  • The first way you can use our calculator is to enter a known value of the angle, and based on that, and you get the required value. The calculator will list the values for cos (x), sin (x), tan (x), csc(x), sec (x) and cot (x) and the values for the functions squared. 
  • You can use the second method if you know the value of one of the functions. By entering the value of the function, sin (x), cos (x), or tan (x), in decimal form, you can get the value of the angle x. Another great option when using our calculator is seeing the calculation steps by pressing the desired result.

Power Reducing Calculator – Example

Following the instructions for the use of our calculator, we will show you how to use it in a straightforward example. We will assume that you have the task of solving a trigonometric expression using all the formulas and rules you have learned so far related to reducing power. Accordingly, the task is:

Find the value of the expression cos2(x) – cos4(x) if you know that x = 35 degrees.
The task has three stages.

  • First, it is necessary to find the value of cos2(x), the value of cos4(x), and their difference.
  • In our calculator at the very top, you can find the option of choosing whether you know the value of the angle or the function. You need to enter the angle value in this field, equal to 35 degrees in this example. Automatically our calculator will throw out solutions for all trigonometric functions, and you need for cos(x).
  • The result value for the cos(x) angle function of 35 degrees is 0.8192. The cos2(x) value for the same angle is 0.6710. In the second segment of the expression, you can find the value for cos4(x) by following these steps:
\left [\cos^{2}(x) \right ]^{2} = \cos^{4}x 

Following this math expression, we arrive at a value of 0.450241. Finally, it is necessary to calculate the value of the difference between these two: 

\left [\cos^{2}(x) \right ]^{2} = \cos^{4}x \Rightarrow 0.6710 - 0.450241 = 0.220759


How do you calculate power reduction?

You can calculate the power reduction applying the formula to simplify the calculation. You can use squares, double angle formulas, and the Pythagorean theorem.

What is cos 4x?

To find the value of cos4x you need to use the following expression: cos (4x) = cos (2x + 2x)

What is the reduction formula for cos?

You can solve a complex formulation of an expression with degree n with the help of the reduction formula. Additionally, you can derive it from the basic formulas of integration. Furthermore, you can find the reduction formula for cos – the cosine function and other trigonometric functions, including sin, tan, csc, cot; Try our Power Reduction Calculator.