If 0 < f ≤ 90 and cos(22f − 1) = sin(7f + 4), what is the value of f?

  f = 3

Step-by-step explanation:

The cosine of one angle is equal to the sine of another angle when the two angles are complementary:

  22f -1 = 90 -(7f +4)

  29f = 87 . . . . . . . . . . add 7f-1

  f = 3 . . . . . . . . . . . . . divide by 29

Besides being complementary, there are other relationships between the angles that will allow the sine of one to match the cosine of the other. Partly, this is a result of the cosine being an even function and the sine being an odd function, as well as the periodic nature of both functions. The graphical solution (attached) shows 11 possible values of f in the allowed range. Of these, only the one shown above is an integer.

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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