Power Reducing Tools

Created By : Jatin Gogia
Reviewed By : Phani Ponnapalli
Last Updated at : Oct 10,2023


Check out our best online free power reducing formula calculator that easily helps to calculate the trigonometric functions with power. For using this calculator easily, give the inputs in the input fields click on the calculate button, and get the answers instantly.

 

To Calculate
Angle

Power Reducing Tools: Looking for an easy tool to understand the power reducing trigonometric functions? Use our power reducing calculator that gives you immediate answers, for that you need to enter the angle that you wish to convert and then you will get the answer of sin2θ, cos2θ, or tan2θ of that angle.

How do we reduce the power of Trigonometric Identities?

In trigonometry, power reduction is estimating the squared value of the trigonometric functions like sin, cos, and tan. We will see the formulas of sin, cos, and tan of trig power reduction.

Formulas of Power Reduction

sin2θ = [1 – cos(2θ) ] / 2
cos2θ = [1 + cos(2θ) ] / 2
tan2θ = [1 – cos(2θ) ] / [1 + cos(2θ) ]

Steps to Calculate the Power Reducing Trigonometric Functions

The simple and easy steps for calculating the reducing values of power. To reduce the power of squared trigonometric functions below the steps carefully.

  • Firstly, we need to determine which trigonometric value we are going to analyze.
  • After that, we need to convert that function by using the formulas that are shown above.
  • Then, calculate the value by entering the angle into the formula.
  • Finally, you will get the answer to the power reduction trigonometric function.

Example:

Question: If the value of θ = 60°, then calculate the value of sin2θ, cos2θ, tan2θ.

Solution:

Given angle θ = 60°

Now we will apply the formulas of sin, cos, tan and simplify them.

sin2θ = [1 – cos(2θ) ] / 2

Substitute the value of θ = 60° in the above formula

sin2 60°= [1 – cos(2 * 60) ] / 2

sin2 60°= [1 – cos(120) ] / 2

sin2 60°= [1 – (-0.5) ] / 2

sin2 60°= [1+0.5] / 2

sin2 60°= 0.75

cos2θ = [1 + cos(2θ) ] / 2

Substitute the value of θ = 60° in the above formula

cos60°= [1 + cos(2 * 60) ] / 2

cos260°= [1 + cos(120) ] / 2

cos260°= [1 + (-0.5) ] / 2

cos260°= [1-0.5] / 2

cos260°= 0.25

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

Substitute the value of θ = 60° in the above formula

tan260° = [1 – cos(2 * 60°) ] / [1 + cos(2 * 60°) ]

tan260° = [1 – cos(120°) ] / [1 + cos(120°) ]

tan260° = [1 – (-0.5) ] / [1 + (-0.5) ]

tan260° = [1.5 ] / [0.5 ]

tan260° = 3

Therfore, the values of sin2θ, cos2θ, tan2θ is 0.75, 0.25, 3.

Use our math calculators for easy and quick answers available at arithmeticcalculators.com. And these calculators are helpful to verify answers of your manual calculations.

Frequently Asked Questions on Power Reducing Tools

1. What do you mean by power reducing?

Power reducing is the type of function that computes the squared trigonometric functions like tan, cos, sin.

2. How do you calculate the power reduction?

For calculating power reduction we use some trig functions.

1. sin2θ = [1 – cos(2θ) ] / 2
2. cos2θ = [1 + cos(2θ) ] / 2
3. tan2θ = [1 – cos(2θ) ] / [1 + cos(2θ) ]

3. How to derive power reduction formulas?

Power reduction trig identities, Power reduction formulas can be derived using double angle and half-angle formulas and Pythagorean identity.

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