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Math Calculators ▶ Power Reducing Formula Calculator

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**Table of Content**

The power reducing formula calculator is a specifically designed trigonometric calculator that is used to reduce and indicate the square, cube, and fourth power trigonometric identities.

The power-reducing identities are used to rewrite the trigonometric angles. It is quickly able to convert the value of the angels sin2θ, cos2θ, and tan2θ in the highest degrees. The power reducing calculator is reducing the power of the trigonometric ratios to the following power.

- Sin2x, Cos2x, Tan2x
- Sin3x, Cos3x, Tan3x
- Sin4x, Cos4x, Tan4x

The power reducing formulas and the procedures are to evaluate the square value of the 3 basic trigonometric ratios. The basic trigonometric ratios are(sin, cos, tan) and we use the power-reducing formula calculator to reduce the value of the identity in the higher units.

In the power reducing formulas, we obtain the second and third versions of *sin4**θ, **cos4**θ, and **tan4*** θ**. We need to understand the value is going to reduce when we are increasing the power of the trigonometric ratios.

The most common trig power reducing identities are given below. We need to remember these identities are also used in the power reducing formula calculator.

- sin2θ = [1 – cos (2θ)] / 2
- sin3θ=(sin2θ)(sinθ)

- sin4θ=(sin2θ)^2

- cos2θ = [1 + cos (2θ)] / 2

- cos3θ=(cos2θ)(cosθ)

- cos4θ=(cos2θ)^2

- tan2θ = [1 – cos (2θ)] / [1 + cos (2θ)]

- tan3θ=(tan2θ)(tanθ)

- tan4θ=(tan2θ)^2

We can understand the concept of the power reducing by the power reducing formula examples:

**Example:**

Formulate the values of *sin**2**θ,**cos**2*** θ,** and

**We can find it by putting the values in the ***sin**2**θ = [1 – cos (2θ)]/2*

*Θ = 30*

*sin**2**θ = [1 – cos (2θ)]/2*

*sin**2** (30°) = [1 – cos (2(30°))]/2*

*sin**2** (30°) = [1 – cos (60°)]/2*

*sin**2** (30°) = [1 – cos (60°)]/2*

*sin**2** (30°) = (1 – 0.5)/2*

*sin**2** (30°) = 0.5/2*

*sin**2** (30°) = 0.25*

*As *sin3θ=(sin2θ)(sinθ)

*sin**3** (30°) = 0.125*

*sin**4** (30°) = 0.0625*

sin4θ=(sin2θ)^2

**The value of cos****2****θ in the identity of power reducing formulas [1 + cos (2θ)]/2.**

*cos**2**θ = [1 + cos (2θ)]/2*

*cos**2 **(30°) = [1 + cos (2(30°))]/2*

*cos**2 **(30°) = [1 + cos (60°)]/2*

*cos**2 **(30°) = (1 + 0.5)/2*

*cos**2 **(30°) = 1.5/2*

*cos**2 **(30°) = 0.75*

*cos 3(30°) = 0.65*

*As *cos3θ=(cos2θ)(cosθ)

*cos**4**(30°) = 0.5625*

cos4θ=(cos2θ)^2

**The value of tan****2****θ in the trigonometric power reduction [1 – cos (2θ)]/ [1 + cos (2θ)]. We get **

*tan**2**θ = [1 – cos (2θ)]/ [1 + cos (2θ)]*

*tan**2 **(30°) = [1 – cos (2(30°)]/ [1 + cos (2(30°)]*

*tan**2 **(30°) = [1 – cos (60°)]/ [1 + cos (60°)]*

*tan**2 **(30°) = [1 – 0.5]/ [1 + 0.5]*

*tan**2 **(30°) = 0.5/ 1.5*

*tan**2 **(30°) = 0.33*

*tan**3**(30°) = 0.1924*

*As *tan3θ=(tan2θ)(tanθ)

*tan**4 **(30°) = 0.111*

tan4θ=(tan2θ)^2

The power-reducing formula calculator can perform all the calculations in the blink of an eye and we can verify all the values by doing the manual calculations.

We can find the values of the trigonometric ratios and their higher power by inserting the value of the angles like 30°,45°, 60°, etc in the trigonometric power reduction calculator. Let’s see how!

**Input:**

- You can enter the value of the angles.
- Enter the value of the trigonometric ratio to get the angle
- After you are done, hit the calculate button

**Output:**

The power reducing calculator is used and we are able to find the following outputs.

- We are able to find the value of trigonometric ratios
- The value of the upper value is also shown

For finding the cos(4x), we need to add the values in the cos(4x)=cos(2x+2x)

The 6 trigonometric identities are Sine, Cosine, Tangent, Secant, Cosecant and Cotangent. They are written as sin, cos, tan, sec, cosec, and cot.

The 3 Pythagorean identities in trigonometry identities are

**sin****2****θ + cos****2****θ = 1****sec****2****θ – tan****2****θ = 1****csc****2****θ – cot****2****θ = 1**

The power reducing formula calculator is used to find the higher powers of the trigonometric ratios and their values. These values can be used to solve the various numerical problems of calculus.

From the source of Wikipedia: List of trigonometric identities, Pythagorean identities

From the source of clarku.edu:Summary of trigonometric identities, Truly obscure identities.