# Which one is not correct? Provide the explanation for each. a. sin1 > sin1° b. sin2 < cos1 c. sin2 > sin1 d. tan1 < tan2

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### 1 Answer

1 radian is 57 degrees to the nearest integer. We don't need a calculator for this as long as we know that `sin(1)>sin(pi/6)=1/2` and `cos(1)>cos(pi/3)=1/2.` These are obvious from either the unit circle or right triangle definitions of the trig functions, and the fact that `pi/6<1<pi/3.`

a) sin 1 > sin 1`^o` is true, since `sin 1>1/2` and `sin 1^o<1/2.` **Choice (a) is true.**

b) Since `sin 2=2sin1*cos1,` this will be true if `2sin1<1.` But `sin 1>1/2` and so `2sin1>1.` **Therefore choice (b) is false.**

c) Again, `sin2=2sin1*cos1,` which is greater than `sin1` if `2cos1>1.` Since `cos(1)>1/2,` **choice (c) is true.**

d) `tan1>0` and `tan2<0,` since `sin(2)>0>cos(2).` **Therefore choice (d) is false.**