2D + D + 1 = sin(2x)
Understand the Problem
The question is asking to solve the equation 2D + D + 1 = sin(2x) for the variable D in terms of x. This involves understanding both algebraic manipulation and trigonometric functions.
Answer
$$ D = \frac{\sin(2x) - 1}{3} $$
Answer for screen readers
The value of $D$ in terms of $x$ is $$ D = \frac{\sin(2x) - 1}{3} $$
Steps to Solve
- Combine Like Terms First, we combine the terms involving $D$ on the left side of the equation: $$ 2D + D = 3D $$
Now, the equation becomes: $$ 3D + 1 = \sin(2x) $$
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Isolate the Term with D Next, we need to isolate the term with $D$. We do this by subtracting 1 from both sides: $$ 3D = \sin(2x) - 1 $$
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Solve for D Now, we solve for $D$ by dividing both sides by 3: $$ D = \frac{\sin(2x) - 1}{3} $$
The value of $D$ in terms of $x$ is $$ D = \frac{\sin(2x) - 1}{3} $$
More Information
The solution shows that $D$ is expressed as a function of the trigonometric sine function. This relationship is useful in various fields, such as physics and engineering, where wave functions often appear.
Tips
- Forgetting to combine like terms before isolating the variable. Always check to group similar terms when possible to simplify the equation.
- Not moving all terms to one side of the equation when isolating the variable. It's important to follow proper algebraic rules to ensure accuracy.
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