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

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In summary, the conversation discusses different strategies for solving the equation 117.72=100sin2x + 28cosx, such as evaluating the right-hand side for different values of x, graphing the equation, and using trigonometric identities to simplify the expression. The conversation also mentions the identity (2cos(x)^2 -1) = sin2x as a potential method for solving the equation.
  • #1
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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  • #2
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.
 
  • #3
use the identity (2cos(x)^2 -1) = sin2x to make it a quadratic equation with cosx instead of x
 
  • #4
(2cos(x)^2 -1) = sin2x

Thats a trig Identity?
 
  • #5
ah my memory was bad that one is for cos2x sorry
 

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

What does the equation "Stuck - 117.72=100sin2x + 28cosx" represent?

The equation represents a mathematical relationship between an unknown variable, x, and the values of sine and cosine. The term "Stuck" does not have a specific mathematical meaning and is likely just a label for the equation.

What is the purpose of the equation "Stuck - 117.72=100sin2x + 28cosx"?

The purpose of the equation is to find the value of the unknown variable, x, that satisfies the equation. This could be used in various applications, such as in physics or engineering problems.

How is "Stuck - 117.72=100sin2x + 28cosx" solved?

The equation can be solved by using algebraic techniques to isolate the variable, x, on one side of the equation. This may involve factoring, applying trigonometric identities, or using other mathematical properties.

What is the significance of the number 117.72 in the equation "Stuck - 117.72=100sin2x + 28cosx"?

The number 117.72 is a constant term in the equation and does not involve the unknown variable, x. It may represent a specific value or measurement in a given problem or scenario.

Can "Stuck - 117.72=100sin2x + 28cosx" have more than one solution?

Yes, depending on the specific values of the constants and the range of values for x, the equation may have multiple solutions. In some cases, there may be an infinite number of solutions.

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