Find the complete solution in radians of each equation. 2 cos^2 θ+sinθ=1

Name: Problem 52, Chapter 14: Algebra 2
Uploaded: 2020-02-24T05:50:28-08:00
Duration: 3 min 39 s
Channel: Jeyasree R T
Description: Find the complete solution in radians of each equation. 2 cos^2 θ+sinθ=1

step 1 complete solution of the equation to cos square theta plus sine theta equals to one. Using this

Find the complete solution in radians of each equation. 2...

Key Concepts

Trigonometric Identities

These are fundamental relationships between trigonometric functions that allow one to rewrite expressions in different forms. In this context, the Pythagorean identity, which relates sin²? and cos²? (namely, sin²? + cos²? = 1), is used to express one function in terms of the other to simplify the equation.

Equation Transformation

This involves rewriting the given trigonometric equation into an equivalent form that is easier to solve. By substituting identities or rearranging terms, the equation is converted into a standard form, such as a quadratic equation, which has well-established solution methods.

Solving Quadratic Equations in Trigonometric Functions

Many trigonometric equations can be manipulated into a quadratic form with respect to a single trigonometric function (e.g., sin? or cos?). Once in this form, standard techniques such as factoring or the quadratic formula can be applied to find the values of the trigonometric function that satisfy the equation.

General Solutions to Trigonometric Equations

Trigonometric functions are periodic, meaning that there are infinitely many solutions. After finding the principal solutions for the equation (for instance, when sin? equals a specific value), the general solution is expressed by incorporating the periodicity, typically adding integer multiples of the period (e.g., 2? for sine and cosine).

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