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Rules of Trigonometric Signs

In this section we will learn about the rules of trigonometric signs. On a plane paper let O be a fixed point. Draw two mutually perpendicular lines XOX and YOY through O divide the plane paper into four quadrants.

We know that, the distance measured from O along XO is positive and that along OX is negative; similarly again, the distance from O along OY is positive and that along OY is negative.

Now, take a rotating line OA rotates about O in the clockwise or anti-clockwise direction and starting from the initial position angle ∠XOA = θ. Depending on the value of θ the final arm OA may be in the first quadrant or second quadrant or third quadrant or fourth quadrant. Take a point B on OA and draw ¯BC perpendicular to OX (or, OX).

Diagram 1:

(i) ¯OC will be positive if it is measured from O along OX

(ii) ¯CB will be positive if it is measured from O along OY

(iii) ¯OB is positive of the final arm OA

Rules of Trigonometric Signs

Diagram 1


Diagram 2:

(i) ¯OC will be negative if it is measured from O along OX

(ii) ¯CB will be positive if it is measured from O along OY

(iii) ¯OB is positive of the final arm OA

Rules of  Signs

Diagram 2


Diagram 3:

(i) ¯OC will be negative if it is measured from O along OX

(ii) ¯CB will be negative if it is measured from O along OY

(iii) ¯OB is positive of the final arm OA

Rules of  Trig Signs

Diagram 3


Diagram 4:

(i) ¯OC will be positive if it is measured from O along OX

(ii) ¯CB will be negative if it is measured from O along OY

(iii) ¯OB is positive of the final arm OA

Rules of Trigonometric Sign

Diagram 4

Therefore, the rules of trigonometric signs of the sides of the right-angled triangle OBC are as follows:

(i) ¯OC will be positive if it is measured from O along OX as shown in the diagram 1 and diagram 4

(ii) ¯OC will be negative if it is measured from O along OX as shown in the diagram 2 and diagram 3

(iii) ¯CB will be positive if it is measured from O along OY as shown in the diagram 1 and diagram 2

(iv) ¯CB will be negative if it is measured from O along OY as shown in the diagram 3 and diagram 4

(v) ¯OB is positive for all positions of the final arm OA.

 Trigonometric Functions





11 and 12 Grade Math

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