Hello tutors this is simple what I would like you to do is write into a handwriting thats it dont add or removed any information's just write the information below into handwriting thats it thank you.

The equation sin() = 1/2 can be represented and solved in three different ways: a) using the right triangle representation, b) using the Cartesian plane representation, and c) using the graph of trigonometric functions representation. Each representation provides unique insights into the problem.

In the right triangle representation, a right triangle with one angle measuring is drawn, and the Pythagorean theorem is used to solve for the missing side, which is the adjacent side. By using inverse sine function or a reference triangle, the two possible values of that satisfy this equation can be found, which are = 30 degrees or = 150 degrees. Therefore, in the right triangle representation, there are two possible values of that satisfy this equation.

In the Cartesian plane representation, the point (cos , sin ) is plotted on the unit circle, and the equation sin = 1/2 represents the y-coordinate of a point on the unit circle. Since the sine function is periodic, the point (cos , sin ) repeats every 360 degrees. Therefore, there are infinitely many values of that satisfy this equation in the Cartesian plane representation.

In the graph of trigonometric functions representation, the graph of y = sin is plotted, and the equation sin = 1/2 represents the point on the graph where y = 1/2. The graph of y = sin oscillates between -1 and 1 and intersects the y-axis at y = 0. Therefore, there are two possible values of that satisfy this equation, which are = 30 degrees or = 150 degrees.

From these three representations, it can be concluded that the equation sin = 1/2 has two possible solutions in the right triangle representation and the graph of trigonometric functions representation, while it has infinitely many solutions in the Cartesian plane representation due to the periodicity of the sine function. This is because the sine function repeats every 360 degrees in the Cartesian plane representation, whereas it has a finite range in the graph of trigonometric functions representation. The equation sin = 1/2 can be solved using different representations, each providing unique insights into the problem. The right triangle representation and the graph of trigonometric functions representation have two possible solutions, while the Cartesian plane representation has infinitely many solutions due to the periodicity of the sine function.

and lastly write below one in same handwriting too: