cos A + sin A = blah blah
why is the sum not always the same when you change the angle (A) in the triangle?
what about (sin A) ^2 + (cos A) ^2
why is the sum always equal to one?
THANK YOU!!
why is the sum not always the same when you change the angle (A) in the triangle?
what about (sin A) ^2 + (cos A) ^2
why is the sum always equal to one?
THANK YOU!!
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your "blah blah" expressions clearly indicates no one can provide a clear explanation. but i'll try to be somewhat (mathematically) concise.
cos(A) represents a value between (and including) -1 to 1.
sin(A) represents a value between (and including) -1 to 1.
since the value of sin(A) and cos(A) are variable, their sum must also change accordingly. Like if you just asked 2 people to pick a number and add them, you are generally going to get a lot of different results (duh).
as to the sin²(A) + cos²(A) always equal to 1; it has to do with the definition of what sine and cosine represent (along with the Pythagorean Theorem)
If you really want to know: pay attention to basic definitions.
**edit...
first, I'm not sure how sine and cosine were explained to you (as there are a lot of different methods - even though the results are the same). So I'm going to hope you have seen the definitions for the 'unit' circle.
That is, sin(A) represents the y-coordinate of a point on a circle where A is an angle with one of the sides passing through the circle ... blah blah (ha ha) [and cos(A) represents the x-coordinate...]
so if you think about it, sin(A) + cos(A) should change
BUT... if you visualize the angle and the circle (sorry I can't draw a pic here), you will see that a right triangle can be formed where the two shorter sides can be sin(A) and cos(A). So the Pythagorean theorem (a²+b²=c²) will lead to strange anomaly you have discovered.
I know that is vague and may not help, but I'm trying...
best of luck
cos(A) represents a value between (and including) -1 to 1.
sin(A) represents a value between (and including) -1 to 1.
since the value of sin(A) and cos(A) are variable, their sum must also change accordingly. Like if you just asked 2 people to pick a number and add them, you are generally going to get a lot of different results (duh).
as to the sin²(A) + cos²(A) always equal to 1; it has to do with the definition of what sine and cosine represent (along with the Pythagorean Theorem)
If you really want to know: pay attention to basic definitions.
**edit...
first, I'm not sure how sine and cosine were explained to you (as there are a lot of different methods - even though the results are the same). So I'm going to hope you have seen the definitions for the 'unit' circle.
That is, sin(A) represents the y-coordinate of a point on a circle where A is an angle with one of the sides passing through the circle ... blah blah (ha ha) [and cos(A) represents the x-coordinate...]
so if you think about it, sin(A) + cos(A) should change
BUT... if you visualize the angle and the circle (sorry I can't draw a pic here), you will see that a right triangle can be formed where the two shorter sides can be sin(A) and cos(A). So the Pythagorean theorem (a²+b²=c²) will lead to strange anomaly you have discovered.
I know that is vague and may not help, but I'm trying...
best of luck
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BUT the sin and cosine values represent an angle in a triangle, this is grade 10 math!
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sin and cosine values do not represent an angle but ratios ( for sin opposite side/ hypotenuse) and for cos adjacent side/ hypotenuse) in a right angle triangle
if we look at sin ^2 A + cos ^2 A as per Pythagorus theorem it is one
if we look at sin ^2 A + cos ^2 A as per Pythagorus theorem it is one
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but sin A + cos A = opposite side/ hypotenuse + adjacent side hypotenuse is not constant this sahll vary as per A
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