Is this correct? The graphs of Sine and Cosine are positive in the first quadrant, but negative in the second, third, and fourth quadrants.?
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:
- WhoLv 72 months ago
nope- they are 90degrees out of phase
- Pramod KumarLv 72 months ago
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.
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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
(x is negative, y is negative )
cosine is negative, sine is negative
(x is positive, y is negative )
cosine is positive , sine is negative
- Anonymous2 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.)