Math Doubts

Signs of trigonometric functions

The value of every trigonometric function is determined by the ratio between lengths of the respective sides of right triangle. Similarly, the sign of the value of each trigonometric ratio is depended on the quadrant. So, it is time to learn the signs of each trigonometric function in all four quadrants.

First Quadrant

The signs of values of all trigonometric functions are positive in first quadrant.

sign of sin function in first quadrant

$(1) \,\,\,$ $\sin{\theta} \,>\, 0$

$(2) \,\,\,$ $\cos{\theta} \,>\, 0$

$(3) \,\,\,$ $\tan{\theta} \,>\, 0$

$(4) \,\,\,$ $\cot{\theta} \,>\, 0$

$(5) \,\,\,$ $\sec{\theta} \,>\, 0$

$(6) \,\,\,$ $\csc{\theta} \,>\, 0$

Second Quadrant

The signs of values of sine and cosecant functions are positive and the remaining functions are negative.

$(1) \,\,\,$ $\sin{\theta} \,>\, 0$

$(2) \,\,\,$ $\cos{\theta} \,<\, 0$

$(3) \,\,\,$ $\tan{\theta} \,<\, 0$

$(4) \,\,\,$ $\cot{\theta} \,<\, 0$

$(5) \,\,\,$ $\sec{\theta} \,<\, 0$

$(6) \,\,\,$ $\csc{\theta} \,>\, 0$

Third Quadrant

The signs of values of tangent and cotangent functions are positive and the remaining functions are negative.

$(1) \,\,\,$ $\sin{\theta} \,<\, 0$

$(2) \,\,\,$ $\cos{\theta} \,<\, 0$

$(3) \,\,\,$ $\tan{\theta} \,>\, 0$

$(4) \,\,\,$ $\cot{\theta} \,>\, 0$

$(5) \,\,\,$ $\sec{\theta} \,<\, 0$

$(6) \,\,\,$ $\csc{\theta} \,<\, 0$

Fourth Quadrant

The signs of values of cosine and secant functions are positive and the remaining functions are negative.

$(1) \,\,\,$ $\sin{\theta} \,<\, 0$

$(2) \,\,\,$ $\cos{\theta} \,<\, 0$

$(3) \,\,\,$ $\tan{\theta} \,<\, 0$

$(4) \,\,\,$ $\cot{\theta} \,<\, 0$

$(5) \,\,\,$ $\sec{\theta} \,>\, 0$

$(6) \,\,\,$ $\csc{\theta} \,>\, 0$



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