Determina el dominio, simetría, periodicidad y cortes con los ejes de la función?

Las funciones seno y coseno tienen su dominio en todo<img src="https://tex.z-dn.net/?f=%5Cmathbb%20R" /> entonces<img src="https://tex.z-dn.net/?f=%5Cmbox%7BDom%7Df%20%3D%20%5Cmathbb%20R" />

Simetrías

Con el eje Y :

<img src="https://tex.z-dn.net/?f=f%28-x%29%20%3D%20%5Ccos%28-2x%29-%5Csin%28-x%29%5C%5C%20%5C%5C%0Af%28-x%29%20%3D%20%5Ccos%282x%29%2B%5Csin%20x%5C%5C%20%5C%5C%0Af%28-x%29%20%5Cneq%20f%28x%29" />

no es simétrico con el eje Y

Periodo :

<img src="https://tex.z-dn.net/?f=f%28x%2BT%29%3Df%28x%29%5C%3B%2CT%5Cneq%200%5C%5C%20%5C%5C%0A%5Ccos%282x%2B2T%29-%5Csin%28x%2BT%29%3D%5Ccos%20%282x%29-%5Csin%20x%5C%5C%20%5C%5C%0A%5Ccos%282x%2B2T%29-%5Ccos%282x%29%3D%5Csin%28x%2BT%29-%5Csin%20x%5C%5C%20%5C%5C%0A-2%5Csin%282x%2BT%29%5Csin%28T%29%3D2%5Ccos%28x%2B%5Cfrac%7BT%7D%7B2%7D%29%5Csin%28%5Cfrac%7BT%7D%7B2%7D%29%5C%5C%20%5C%5C%0A-2%5Csin%282x%2BT%29%5Csin%28%5Cfrac%7BT%7D%7B2%7D%29%5Ccos%28%5Cfrac%7BT%7D%7B2%7D%29%3D%5Ccos%28x%2B%5Cfrac%7BT%7D%7B2%7D%29%5Csin%28%5Cfrac%7BT%7D%7B2%7D%29%5C%5C%20%5C%5C%0A-2%5Csin%282x%2BT%29%5Ccos%28%5Cfrac%7BT%7D%7B2%7D%29%3D%5Ccos%28x%2B%5Cfrac%7BT%7D%7B2%7D%29%5Cvee%20T%3D2k%5Cpi%5C%5C%20%5C%5C%0A%0A" />

<img src="https://tex.z-dn.net/?f=-4%5Csin%28x%2B%5Cfrac%7BT%7D%7B2%7D%29%5Ccos%28x%2B%5Cfrac%7BT%7D%7B2%7D%29%5Ccos%28%5Cfrac%7BT%7D%7B2%7D%29%3D%5Ccos%28x%2B%5Cfrac%7BT%7D%7B2%7D%29%5Cvee%20T%3D2k%5Cpi%5C%5C%20%5C%5C%0A-4%5Csin%28x%2B%5Cfrac%7BT%7D%7B2%7D%29%5Ccos%28%5Cfrac%7BT%7D%7B2%7D%29%3D1%5Cvee%20T%3D2k%5Cpi%5C%5C%20%5C%5C%0A%5Ctext%7BSi%20%7Dx%3D-T%2F2%20%5Ctext%7B%20entonces%20%7D-4%5Csin%28x%2B%5Cfrac%7BT%7D%7B2%7D%29%5Ccos%28%5Cfrac%7BT%7D%7B2%7D%29%3D1%20%5Ctext%7B%20No%20se%20cumple%20%7D%5C%5C%0A%5Ctext%7BPor%20lo%20tanto%20%7DT%3D%5Cmin%5C%7B2k%5Cpi%3A%5Ck%5Cin%20%5Cmathbb%20Z%5C%7D%20%5Ctext%7B%20y%20%7D%20T%5C%20%5Ctextgreater%20%5C%200%5C%3B%20%2C%20%5Ctext%7B%20es%20decir%20%7D" /> <img src="https://tex.z-dn.net/?f=%5Cboxed%7BT%3D2%5Cpi%7D" />.