Trig question

[myair]

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For all the y, the cos y is equal to which of the following?

sin y
sin (-y)
cos (-y)
sin y+ cos y
cos (y+pie)

how did they got the answer?cos (-y)

help me please 🙂

 

[Blarelli]

It is because y=cos(t) is an even trigonometric function, so cos (-t)=cos(t). Can't tell you the hows or anything beyond that.

 

[klutzy1987]

Because cosine is positive in quadrants 1 and 4 and is negative in quadrants 2 and 3. Therefore anything that falls out in quadrant one, if you negate it, it will come out in 4.Therefore Cosine👍=Cosine(-y). I know it isnt very clear. If you still have trouble just question and i will try to make it a little clearer.

 

[adizzle87]

For all the y, the cos y is equal to which of the following?

sin y
sin (-y)
cos (-y)
sin y+ cos y
cos (y+pie)

how did they got the answer?cos (-y)

help me please 🙂

Try drawing the 4 quadrants and draw a triangle having a +1 slope and a -1 slope (.25Pi radians and -.25Pi radians, respectively). You will notice that adjacent/hypotenuse in both situations have the same value since the hypotenuse always stays positive and the adjacent side which is shared is positive as well.

 

[Streetwolf]

For all the y, the cos y is equal to which of the following?

sin y
sin (-y)
cos (-y)
sin y+ cos y
cos (y+pie)

how did they got the answer?cos (-y)

help me please 🙂

By taking the negative of the variable, you are heading in the opposite direction on the circle. Since you start at (1,0) and go counterclockwise, the negative variable starts you at (1,0) and brings you clockwise. The former goes above the x-axis while the latter goes below. This just affects the y-coordinates. Since cosine is the x-coordinate trig function, it doesn't get affected. Thus cos👍 is the same as cos(-y).