write the equation of the following secant and cosecant functions (without a phase shift)\n1.\n2.\n3.

Explanation:

Step1: Recall general form of secant and cosecant functions

The general form of a secant or cosecant function without a phase - shift is $y = A\sec(Bx)$ or $y=A\csc(Bx)$. The period of $y = \sec(x)$ and $y=\csc(x)$ is $2\pi$, and for $y = \sec(Bx)$ and $y=\csc(Bx)$ the period is $T=\frac{2\pi}{|B|}$. Also, the amplitude of secant and cosecant functions is not defined in the same way as for sine and cosine, but $|A|$ affects the vertical stretch or compression.

Step2: Analyze the period of the given functions

Since no phase - shift is mentioned and we assume the standard period of $2\pi$ for the basic secant and cosecant functions (i.e., $B = 1$) and no vertical stretch or compression (i.e., $A = 1$).

1. For the secant function, the equation is $y=\sec(x)$ and for the cosecant function, the equation is $y = \csc(x)$.
2. For the secant function, the equation is $y=\sec(x)$ and for the cosecant function, the equation is $y=\csc(x)$.
3. For the secant function, the equation is $y=\sec(x)$ and for the cosecant function, the equation is $y=\csc(x)$.

Answer:

1. Secant: $y=\sec(x)$; Cosecant: $y=\csc(x)$
2. Secant: $y=\sec(x)$; Cosecant: $y=\csc(x)$
3. Secant: $y=\sec(x)$; Cosecant: $y=\csc(x)$