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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers.
Know more

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.