I have seen students cramming the signs of Trigonometry Functions ( sinϴ, cosϴ, tanϴ, cosecϴ, secϴ, cotϴ) in four Quadrants. Very few students know the concept behind it. But *Adhyan Innovative Learning* always promote conceptual knowledge hence below mentioned is the concept behind signs.

Above shown is a Unit Circle means a simple circle with Radius=1 , 1 can have any measuring unit (mm,cm,m etc). AC is radius and BC is a perpendicular drawn from point C on a simple line passing from the center of the circle. Let us call this line as x axis and a line perpendicular to x axis called as y axis.

We see a triangle is formed where AC is the Hypotenuse, BC is the Perpendicular and AB is the Base. Let us call the angle between AC and AB as ϴ.

**Now By Definition,**

sinϴ = Perpendicular/Hypotenuse

= BC/AC

As this is a Unit Circle which means AC=1 thus

sinϴ = BC

Now If we understand what is BC it is actually Projection of AC on y axis which implies Sinϴ is Projection of AC on y axis

Hey we just understood what is Sinϴ.. that’s so easy ..

Similarly

cosϴ =Base/Hypotenuse

=AB/AC

As this is a Unit Circle which means AC=1 thus

cosϴ =AB

And AB is nothing but Projection of AC on x axis which implies Cosϴ is Projection of AC on x axis.

Signs of Sinϴ,Cosϴ in the 4 Quadrants

As we understood above Sinϴ is Projection of AC on y axis and Cosϴ is Projection of AC on x axis

- In Quadrant 1 (Filled in Green) both y and x are positive and thus Sinϴ, Cosϴ both have positive values.
- In Quadrant 2 (Filled in Yellow) y is positive thus Sinϴ is positive, but x is negative so Cosϴ has negative value.
- In Quadrant 3 (Filled in Orange) both y and x are negative and thus Sinϴ, Cosϴ both have negative values.
- In Quadrant 4 (Filled in Blue) y is negative and thus Sinϴ is negative and x is positive so Cosϴ has positive value.

Now we can easily calculate signs of tanϴ, cotϴ, cosecϴ, secϴ..

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