So I just have a question that I am not sure about.
Why is the maximum possible value for sinx 1 and then there are no solutions?
could someone please try their best to explain this concept to me and the reason why this is true?
Thanks in advance!
Hello skeske1234See the attached diagram.Why is the maximum possible value for sinx 1
Imagine a point that starts at the point on the -axis, and moves anticlockwise around a circle, centre , radius unit.
As it does so, the line rotates through an angle , where initially, and radians when has made one complete rotation.
Then the definition of is the -coordinate of at any moment: in my diagram. (And is the -coordinate of .)
Since P is restricted to lying on the circle, its - and -coordinates always lie between and . Hence the maximum and minimum values of and are and respectively.
Do you mean no solutions to the equation ? Because if you do, that's not true. As you'll see from my diagram, (and so is , , ... and so on.)and then there are no solutions?
Grandad
I don't know what you mean by "and then there are no solutions", but I think you mean to ask why sine never takes on values that are larger than 1.
Think back to the definition of the sine. For a right triangle, isn't the sine ratio equal to "(opposite) over (hypotenue)"? For a right triangle, isn't the hypotenuse always the longest of the sides?
Once you get to viewing the sine as a function, rather than a ratio of sides of a right triangle, you can let the angle be ninety degrees (which obviously wouldn't work in a right triangle), and get a value of "1" for the sine.