Math II Question

Archive SAT Subject Test Preparation
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<p>Today, I took the diagnostic test in the Barron’s Math II book and received a 760. I went over all my mistakes and dont understand one question, 42. It states: If A=arctan(-3/4) and A+B=315, then B=… </p>

<p>When I did the arctan on my calculator, it yielded a value of -36.87, so I added 180 to it because it would have the same tangent, getting 143.13. Then I subtracted that from 315 and got 171.87, one of the answers. The answer key says that the answer is 351.87 because when you do 315-tan(-3/4), you get that when the arctan is -36.87. I dont understand this question because arent there an infinite amount of values that satisfy arctan(-3/4). Both my approach and theirs were correct since that expression is applicable to so many angles.</p>

<p>Thanks for the help in advance.</p>

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<p>y u add 180? you seem to be overthinking this. this is a calculator problem, no thinking required. </p>

<p>do this on your calc: arctan(-3/4) or arctan(-.75) make sure your calc is on degrees.</p>

<p>arctan(-.75)= -36.87</p>

<p>-36.87 +B = 315
B= 315 + 36.87
B= 351.86</p>

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<p>but arent there an infinite number of angles that satisfy arctan(-3/4) that’s why I added 180 just out of convenience to make it positive… I dont see why it should change the answer A is still arctan(-3/4) even if I add 180 thats what I dont understand</p>

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<p>I think @collegebound is correct!</p>

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<p>I think @Dondav is correct</p>

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<p>That’s just an awful question. (I think jman010295 is correct!)</p>

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<p>hahahahaha finally someone who agrees with me!!!</p>

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<p>The inverse tangent function on the calculator has a range restricted to
-90º<y<90º, the principle values. Thus A can be only -36.87º.</p>

<p>edit:
i looked up the problem and the “t” in tan^-1 is not uppercase indicating that the range is restricted to the principle values, so i’m assuming this is an oversight on the testmaker’s part.</p>

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<p>But the question clearly hasn’t restricted the answer to the principle values, so both answers should be valid.</p>

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<p>thats why both answers are not given A,B,C,D answers…</p>