Solve each equation on the interval 0 ≤θ<2 π. tan^2 θ=(1)/(3)

Name: Problem 14, Chapter 7: Precalculus
Uploaded: 2020-07-13T06:00:35-08:00
Duration: 1 min 1 s
Channel: Amit Srivastava
Description: Solve each equation on the interval 0 ≤θ<2 π. tan^2 θ=(1)/(3)

step 1 to solve 10 square theta is equal to 1 divided by 3 where theta belongs to closed interval 0 to

Solve each equation on the interval 0 ≤θ<2 π. tan^2...

Key Concepts

Square Root Property in Equations

When an equation involves the square of a trigonometric function, taking the square root of both sides introduces both positive and negative solutions. It is crucial to consider both cases in order to capture all the angles that satisfy the original equation. This property is often used in solving equations where the trigonometric function is squared, leading to two separate equations to solve.

Reference Angles

A reference angle is the acute angle that a given angle makes with the horizontal axis. It is used to determine the values of trigonometric functions for angles in any quadrant by relating them to their acute counterpart in the first quadrant. This concept simplifies solving trigonometric equations by allowing one to first solve for the acute angle corresponding to the trigonometric value, then determining the appropriate angles in all relevant quadrants.

Trigonometric Equations

Trigonometric equations involve finding the angles that satisfy a given relationship among trigonometric functions. Solving these equations often requires using identities, inverse functions, and the periodic nature of trigonometric functions to identify all possible solutions within a given interval.

Properties of the Tangent Function

The tangent function, defined as the ratio of sine to cosine, is unique among trigonometric functions because it is periodic with a period of ? rather than 2?. This means that its values repeat every ? radians. Understanding its behavior, including its undefined points where cosine is zero and the symmetry about the origin, is essential when solving equations involving tangent.

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