How Do I Solve the Equation 117.72 = 100sin2x + 28cosx for x?

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Homework Help Overview

The discussion revolves around solving the equation 117.72 = 100sin2x + 28cosx for the variable x, which involves trigonometric functions. Participants are exploring methods to find the angle that satisfies this equation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest evaluating the right-hand side of the equation for assumed values of x, graphing the equation, and using trigonometric identities to transform the equation into a potentially solvable form. There is also a discussion about the validity of a specific trigonometric identity.

Discussion Status

The discussion is active with various approaches being proposed, including graphical methods and algebraic manipulation. Some participants are clarifying the use of trigonometric identities, indicating a collaborative exploration of the problem.

Contextual Notes

There is a mention of potential confusion regarding trigonometric identities, which may affect the approach to solving the equation. Participants are navigating through different interpretations and methods without reaching a consensus.

Todd0012
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Stuck please help -- 117.72=100sin2x + 28cosx

Im trying to find an angle and I am stuck

117.72=100sin2x + 28cosx

What do i do now?
 
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You can always assume a value of x and evaluate the RHS of the equation to see if it equals the LHS.

You can graph the RHS of the equation for different values of x, and then draw a line y= 117.72 and use the intersection points to estimate the values of x which are the solutions.

You can use trig identities on the RHS to see if you obtain an equivalent expression in x which may be more amenable to solution.

Take yer pick.
 
use the identity (2cos(x)^2 -1) = sin2x to make it a quadratic equation with cosx instead of x
 
(2cos(x)^2 -1) = sin2x

Thats a trig Identity?
 
ah my memory was bad that one is for cos2x sorry
 

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