Power Reducing Calculator

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 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

cos² 60°= [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 Calculator

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 formulas can be derived using double angle and half-angle formulas and Pythagorean identity.