Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

# Is this correct? The graphs of Sine and Cosine are positive in the first quadrant, but negative in the second, third, and fourth quadrants.?

Update:

Thank you all who answered, I am very grateful!

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All Silly Tom Cats...Q1 Q2 Q3 Q4

i.e. sine, cosine and tangent are positive in Q1

Only sine is positive in Q2

Only tangent is positive in Q3

Only cosine is positive in Q4

This should help:

https://www.onlinemathlearning.com/trig-equations-...

:)>

•  nope- they are 90degrees out of phase

• For determining Positivity / negativity of  the graph of trigonometrical ratios, there is a simple rule.

"sine is represented by y-axis, and cosine is represented by x-axis"

It means sin is positive if y axis is positive i.e. in First and Second Quadrants  and sin is negative in Third and Fourth Quadrants.  Similarly cos (ie x-axis) is  positive in First and Fourth quadrants, while cos (x-axis) is negative in Second and Third Quadrants.

• Take sin x. positive in first quadrant

sin (x+pi/2)= sin x cos pi/2+ cos x sin pi/2=cos x= positive. Second quadrant.

sin(x+pi)= sin x cos pi+ cos x sin pi= - sin x. Third quadrant

sin (2 pi -x)= sin 2pi cos x- cos 2pi sin x=-sin x. Fourth quadrant. It is negative.

cox is positive in first quadrant.

cos (x+pi/2)= - sin x. Negative in second quadrant.

cos (x+pi)= cos x cos pi= -cos x. negative in the third quadrant

cos (2pi-x)= cos 2pi cos x= cos x. +ve in the fourth quadrant.

• Of Course, it's incorrect.

Cosine is the same as the x-coordinate on the unit circle

Sine is the same as the y-coordinate on the unit circle

so in Q1

(x is positive, y is positive )

cosine is positive , sine is positive

in Q2  ,

(x is negative ,  y is positive)

cosine is negative , sine is positive

in Q3

(x is negative, y is negative )

cosine is negative, sine is negative

in Q4

(x is positive, y is  negative )

cosine is positive ,   sine is negative

• Anonymous
2 months ago

I don't believe that's correct.  It seems to me they're 90 degrees out-of-phase with each other, so one starts at the origin and climbs into the positive range while the other is at its lowest value, beginning a climb toward zero.  So they can't both always be positive or negative, together.  They're going to be opposite each other at a couple different points.

(But it's been a long time, and maybe my memory is a bit fuzzy.)