HELP!! Trigonometry!!! PLEASE!
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HELP!! Trigonometry!!! PLEASE!

[From: ] [author: ] [Date: 11-12-21] [Hit: ]
!-your blah blah expressions clearly indicates no one can provide a clear explanation. but ill 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,......
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!!

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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

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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

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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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