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