College

Express [tex]\sin \left(\frac{18}{20}\right)[/tex] in terms of [tex]m[/tex] and [tex]x[/tex].

[tex]\sin \left(\frac{18}{20}\right) = m < x[/tex]

Answer :

We begin by evaluating the expression

[tex]$$
m = \sin\left(\frac{18}{20}\right).
$$[/tex]

Since the sine function (with the argument in radians) produces a value between [tex]$-1$[/tex] and [tex]$1$[/tex], calculating the sine of [tex]$\frac{18}{20}$[/tex] yields

[tex]$$
m \approx 0.783327.
$$[/tex]

Next, we need to choose a number [tex]$x$[/tex] such that

[tex]$$
m < x.
$$[/tex]

A common and simple choice is

[tex]$$
x = 1,
$$[/tex]

because it is clear that

[tex]$$
0.783327 < 1.
$$[/tex]

Thus, the final result is

[tex]$$
\sin\left(\frac{18}{20}\right) \approx 0.783327 \quad \text{and} \quad 0.783327 < 1.
$$[/tex]

This completes the step-by-step solution.