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Doug C.'s Resources

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Hi Liz,    The correct answer is P and Q. See the following graph to get the idea.   https://www.desmos.com/calculator/a4owjrypmf   How to make the decision depends on the techniques you have available to you. Here is what I did on the graph above.   The...

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Hi Seth,   See the following graph to convince yourself that on the interval from [0, 2pi) this equation has 8 solutions.   https://www.desmos.com/calculator/4qqtxxk6wr   The question is how to you find those solutions algebraically?   Start by...

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One way to locate point M is to use coordinate geometry. See this graph:   https://www.desmos.com/calculator/7puz1lavso   Using this graph you can see that the coordinates of the midpoint of diagonal AC are (5.5,4). Now write the equation of the line through B and that...

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Hi Diamond,   See this picture to get the idea:    https://www.desmos.com/calculator/dhmbl3yt9h   The d1 in the diagram represents 1/2 of one of the diagonals. Use the cos 20 to find 1/2 of the other diagonal.  Those results can be doubled...

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Hi Jasmine,   Try replacing sin(a+b) with sina cosb + cosa sinb.   Replace tana with sina/cosa.   Replace tanb with sinb/cosb.   Now you have a complex fraction. There are a couple ways to go from there.    I like to multiply...

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Without a diagram it is difficult to surmise exactly what is going on, but perhaps the diagram looks something like this:   https://www.desmos.com/calculator/nkasdz0nbx   If that looks correct you might be able to sift through the equations and determine how the value of...

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Hi Michael,   Think of the reference angle and associated triangle for angle B. Its opposite side will be -1 with a hypotenuse of 3. Use Pythagorean theorem to get adjacent side: 2√2 (which will be negative in QIII). This means the cos B = -2√2/3.   There are several different...

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Hi Gnarls,   Since tan = sin/cos and sec = 1/cos you can write:   (sinx/cosx) + (1/cosx) --------------------------           cosx   Think of this as a complex fraction which can be simplified by multiplying top and bottom...

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Hi Zakia,   My guess is that this question is expecting you to treat f(x) as some unknown parent function, and then describe the effect on the parent that the numbers 2 and -1 for F(x) have on the parent. Likewise for G(x) what effect do the 1 and -2 have on the parent.   For...

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