JEE Advanced Physics: Trigonometry (Mathematical Tools in Physics) questions with solutions

Q1. Find the approximate value of x, where x = sin(1 deg) * cos(1 deg).

1. pi/90
2. 2
3. pi/180
4. pi/45

Answer: pi/180

Using the identity sin(A)cos(A) = (1/2)sin(2A): sin(1 deg)cos(1 deg) = (1/2)sin(2 deg). For small angles in radians, sin(theta) approx theta, so sin(2 deg) approx 2 deg in radians = 2 * pi/180 = pi/90. Therefore x approx (1/2)(pi/90) = pi/180.