Use a coterminal angle to find the exact value of the expression. Do not use a calculator. cot 420^circ

We know that 420 degrees is equivalent to 360 degrees plus 60 degrees or 1 full rotation plus 60 degrees. Thus, the coterminal angle to 420 degrees is -300 degrees (adding or subtracting multiples of 360 degrees does not change the position of the angle). Now, we can find the exact value of cot(-300 degrees) by using the unit circle. Cotangent is equal to the cosine over the sine, and the cosine of -300 degrees is the same as the cosine of 60 degrees (cosine is an even function, meaning it is symmetric about the y-axis), which is 1/2. Similarly, the sine of -300 degrees is the same as the sine of 60 degrees (sine is an odd function, meaning it changes sign when the angle is reflected about the y-axis), which is ?3/2. Therefore, cot(-300 degrees) = 1/?3 = ?3/3. So, the exact value of cot 420 degrees is also ?3/3 since -300 degrees is a coterminal angle that gives the same ratio.