Explain why the value of sine ratio for an acute angle of a right triangle must always be a positive value less than 1

See below.

The sine ratio is the ratio of the opposite side over the hypotenuse in a right triangle. The hypotenuse is always the largest side of a triangle.

Therefore, the denominator will always be the largest. If the denominator is larger than the numerator, it will be a number less than one.

And it will be positive because it is an acute angle so the triangle when plotting in the unit circle would only be in the first quadrant. All values in the first quadrant are positive.

In this exercise we have to explain why the sine value must always be positive, for this is because of the first quadrant.

How does the sine work?

The sine of an angle will always be positive in the 1st and 2nd quadrants and negative in the 3rd and 4th, always under the ordinate (y) axis.

In this way we can say that this occurs because:

Will be positive because it is an acute angle so the triangle when plotting in the unit circle would only be in the first quadrant. All values in the first quadrant are positive.

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F(g(3))
find g(3)
g(3)=3^2+1=9+1=10

f(g(3))=f(10)
f(10)=2(10)+3=20+3=23

f(g(3))=23