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

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To solve the equation 117.72 = 100sin2x + 28cosx, one approach is to graph the right-hand side for various x values and find intersection points with the line y = 117.72. Another method involves using trigonometric identities to transform the equation, such as substituting sin2x with 2cos²x - 1, leading to a quadratic equation in terms of cosx. Evaluating specific x values can also help determine if they satisfy the equation. Overall, combining graphical and algebraic methods can effectively identify solutions for x.
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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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