Angelica and Graciella are working together to find the sine and cosine of A for ABC. They are given that tan A=3/4. Angelica says the tangent is the ratio of the length of the leg opposite A over the length of the leg adjacent to A. This means BC must have a length of 3 units and AC must have a length of 4 units. They can find the length of AB using the Pythagorean Theorem and then use it to find the sine and cosine ratios.

Graciella says that they cannot find the length of any side of the triangle and, therefore, cannot find the ratios for sine and cosine.

Both students have errors in their reasoning.

1. identify the mistake Angelica made in her reasoning. provide an example that shows why she is incorrect.

2. identify the mistake that Graciella made in her reasoning. Explain why she is incorrect.

3. Find the ratios for the sine and cosine of A. Explain your process.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

its a trick question

step-by-step explanation:

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hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb