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Mathematics

Signs of trigonometric functions in different quadrants

In this Class 12 Mathematics topic from the Trigonometric Functions chapter, students learn how the signs of sine, cosine, tangent and their reciprocal functions change across the four quadrants of the Cartesian plane. They connect an angle’s terminal side with the coordinates and reference angle, identify which functions are positive or negative in each quadrant, and apply these rules to simplify expressions, evaluate trigonometric ratios, and check the consistency of solutions.

Easy · Level 1 · 1 questions

Practice questions

01What is the sign of \(\sin x\) in the first quadrant?

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Answer and explanation

Correct answer: C. Positive

The governing concept is the sign pattern of trigonometric functions in the four quadrants. In the first quadrant, an angle lies between \(0\) and \(\pi/2\), so its unit-circle point has both x- and y-coordinates positive. Since sine is the y-coordinate, \(\sin x>0\) throughout the first quadrant. Therefore, option C, Positive, is correct. Zero occurs on the x-axis at boundary angles such as 0 or \(\pi\), not inside the first quadrant. A negative sine value occurs in the third and fourth quadrants, while undefined is not the correct description for sine at ordinary first-quadrant angles.

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Signs of trigonometric functions in different quadrants

Practice questions

01What is the sign of \(\sin x\) in the first quadrant?पहले चतुर्थांश में \(\sin x\) का चिन्ह क्या होता है?

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01What is the sign of \(\sin x\) in the first quadrant?