QR: Trig question

[ddstobe]

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What is the different between cos(116), -cos(116), cos(-116), sin(116), -sin(116) etc...I'm so confused with the signs

I found this question from destroyer #26, thx

 

[UCB05]

What is the different between cos(116), -cos(116), cos(-116), sin(116), -sin(116) etc...I'm so confused with the signs

I found this question from destroyer #26, thx

cos(x) is a symmetric function that is reflected about the y axis. For us, this means cos x = cos (-x)
cos (-116) = cos (116)

sin(s) is a symmetric function that has a reversal of value at the y axis. This means sin (-x) = -sin x
sin (-116) = -sin(116)

 

[ddstobe]

I still don't understand why cos(116) = -cos(64). What is the different of having the neg sign in front of the cos and within the ()? Could you explain it a little more? thx

 

[UCB05]

I still don't understand why cos(116) = -cos(64). What is the different of having the neg sign in front of the cos and within the ()? Could you explain it a little more? thx

There's two things you need to know to answer that question.
On the second part of your question: look at a normal cosine graph. Can you see how it's symmetrical about the y axis? starting from x=0, look at the value of cosine at 45 degrees. Now look at the value of cosine at -45 degrees. They're the same. For every value of x, cos(x) has the same value as cos(-x). cos (-x) = cos (x)

Now for the first part of your question: look at the cosine graph again. See how it makes a full cycle every 360 degrees? That means cos (x) = cos (x+360). Now notice that every 180 degrees, it flips its sign but has the same absolute value, so that cos (x) = -cos (x+180)

so for x = -64
cos (-64) = -cos (-64+180) = -cos (116)
BUT because of the cos identity cos (-64) = cos (64),
cos (64) = -cos (116) or
-cos (64) = cos (116)