For example, the first question, first of all, the basic shapes of the two figures must be the same, just a matter of how much they can overlap. To overlap, you can only consider the position of the peak without considering the function deformation (you can also consider the trough, but you should pay attention to the fact that there are two zeros in a cycle, so the superposition of zeros does not necessarily coincide with the waveform). The position of the peak is easy to determine. The peak of sin appears when inside is equal to π/2, and the peak of cos appears when inside is equal to 0. In the first problem, when the peak of the former function appears as 0 in cos, it is solved as x= -pi/6, and when the peak of the latter function appears as pi/2 in s in, it is solved as x = pi/4. In order to make these two positions coincide, it is obvious that the latter function shifts pi/4-(-pi/6) = pi * 5/65438 to the left.
After the latter question is translated, the function formula is y = sin( x+pi/3), and then expansion is equivalent to changing the X band to 2x. So the result is y = sin(2x +pi/3). Or you can use a method similar to the 1 question: the peak value of the original function is at pi/2, at pi/6 after translation, at pi/ 12 after scaling, and there is only one peak value in the option at pi/ 12.
Above, pay attention to the periodicity of trigonometric function, so the addition and subtraction periods of the answers are correct. If you move the right and left by an appropriate distance, the result is the same. Think about it yourself.