<p>If Sin A = cos B, then which of the following must be true?</p>
<p>A. A=B
B. A=2B
C. A=B+45
D. A=90-B
E A=B+180</p>
<p>I chose answer A because Sin(45)=cos(45), so 45=45, and A=B.</p>
<p>The PR book says that the answer is D because sin(90)=cos(0) if A=90 and B=0. So then A=90-B.</p>
<p>Help? Both answers seem legit to me.</p>
<p>The answer you wanted to choose is only right some of the time. I’ll just give a counterexample for all the wrong answers.</p>
<p>Answer A: sin 30=.5=cos 60. 30≠60, so answer is wrong.
Answer B: works with the above example, but not with sin 45=.707=cos 45. 45≠(2)(45)
Answer C: see explanation of answer A. 30≠60+45
Answer D: works with both of the above examples, and for any angle you try. Some more examples: sin 100=.985=cos (-10). 100=90-(-10).<br>
sin 22=.375=cos 68. 22=90-68
sin 87956=.899=cos (-87866). 87956=90-(-87866)
Answer E: I’m not going to bother. The first example disproves it.</p>
<p>This question is basically testing your knowledge of trignometric identities- namely the Cofunction Identity which is stated as:</p>
<p>sin(90-X)= cosX
sec(90-X)= cscX
tan(90-X)= cotX</p>
<p>(and vice versa)</p>
<p>Also, note that the same rule applies to angles measured in radians.</p>
<p>if you sketch a right triangle and you know that sine = opp/hyp and cos = adj/hyp you’ll notice that whatever angle you put the other will be ninety minus that angle. never try 45-45-90 'cause they’ll trick you.
sin(90-X)= cos(X) would work for the case of a 45-45-90 which means that this “must be true” unlike option A that wouldn’t work for any other angle…</p>
<p>This is testing the cofunction pairs.</p>
<p>What the poster above said is correct (and perhaps the better way to solve the problem), but I think this might help you understand it better, and at the very least it’s something that you should know.</p>
<p>The cofunction pairs are </p>
<p>sin/cos
sec/csc
tan/cot</p>
<p>If two cofunctions are equal to eachother, then the sum of their angles is 90.</p>
<p>ex. sin 6a = cos 3a
9a = 90
a = 10</p>
<p>your case is more basic, you have sin a = cos b
so a + b = 90
change it to a = b - 90 and you have your answer d</p>