Now consider the product of a nonzero rational number and an irrational number. Again, assume x = 9, where a and b are integers and b +0. This time let y be an irrational number. If we assume the product x. y is rational, we can set the
product equal to where mand n are integers and n # 0. The steps for solving this equation for y are shown.
Statement
Reason
y=
y=
..y=
substitution
b
G
a
multiplication property of equality
Simplify.
y=
m. b
no
Based on what we established about the classification of y and using the closure of integers, what does the equation tell
you about the type of number y must be for the product to be rational? What conclusion can you now make about the
result of multiplying a rational and an irrational number?

You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function.how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions