Signs of Trigonometric functions in Quadrants
Fact-checked:
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.
$(1) \,\,\,$ $\sin{\theta} \,>\, 0$
$(2) \,\,\,$ $\cos{\theta} \,>\, 0$
$(3) \,\,\,$ $\tan{\theta} \,>\, 0$
$(4) \,\,\,$ $\cot{\theta} \,>\, 0$
$(5) \,\,\,$ $\sec{\theta} \,>\, 0$
$(6) \,\,\,$ $\csc{\theta} \,>\, 0$
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.
$(1) \,\,\,$ $\sin{\theta} \,<\, 0$
$(2) \,\,\,$ $\cos{\theta} \,<\, 0$
$(3) \,\,\,$ $\tan{\theta} \,<\, 0$
$(4) \,\,\,$ $\cot{\theta} \,<\, 0$
$(5) \,\,\,$ $\sec{\theta} \,>\, 0$
$(6) \,\,\,$ $\csc{\theta} \,>\, 0$
