FAQs on Signs of the Trigonometric Functions Video Lecture  Mathematics (Maths) for JEE Main & Advanced
1. What are the signs of the trigonometric functions? 

Ans. The signs of the trigonometric functions depend on the quadrant in which the angle is located. In the first quadrant, all trigonometric functions (sine, cosine, and tangent) are positive. In the second quadrant, only the sine function is positive, while the cosine and tangent functions are negative. In the third quadrant, only the tangent function is positive, while the sine and cosine functions are negative. In the fourth quadrant, only the cosine function is positive, while the sine and tangent functions are negative.
2. How do I determine the sign of the sine function? 

Ans. To determine the sign of the sine function, you need to consider the quadrant in which the angle is located. In the first and second quadrants, the sine function is positive. In the third and fourth quadrants, the sine function is negative. Additionally, since the sine function is an odd function, its sign is also determined by the symmetry of the angle with respect to the xaxis. If the angle is above the xaxis, the sine function is positive. If the angle is below the xaxis, the sine function is negative.
3. What is the sign of the cosine function? 

Ans. The sign of the cosine function also depends on the quadrant in which the angle is located. In the first and fourth quadrants, the cosine function is positive. In the second and third quadrants, the cosine function is negative. Similar to the sine function, the cosine function is an even function, so its sign is determined by the symmetry of the angle with respect to the yaxis. If the angle is to the right of the yaxis, the cosine function is positive. If the angle is to the left of the yaxis, the cosine function is negative.
4. How can I determine the sign of the tangent function? 

Ans. The sign of the tangent function can be determined by analyzing the signs of the sine and cosine functions. In the first quadrant, where both sine and cosine are positive, the tangent function is also positive. In the second quadrant, where sine is positive and cosine is negative, the tangent function is negative. In the third quadrant, where both sine and cosine are negative, the tangent function is positive. In the fourth quadrant, where sine is negative and cosine is positive, the tangent function is negative.
5. Are there any exceptions to the signs of the trigonometric functions? 

Ans. Yes, there are exceptions to the signs of the trigonometric functions. One important exception is when the angle is equal to 0 degrees or 180 degrees. In these cases, the sine function is 0, the cosine function is positive, and the tangent function is also 0. Additionally, at angles of 90 degrees and 270 degrees, the sine function is positive, the cosine function is 0, and the tangent function is undefined. These exceptions should be considered when determining the signs of the trigonometric functions.