Homework Help

Which one is not correct? Provide the explanation for each. a. sin1 > sin1° b. sin2...

user profile pic

madmoni06 | Student | (Level 1) Honors

Posted April 5, 2013 at 6:59 PM via web

dislike 0 like

Which one is not correct? Provide the explanation for each.

a. sin1 > sin1°

b. sin2 < cos1

c. sin2 > sin1

d. tan1 < tan2

1 Answer | Add Yours

user profile pic

degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted April 5, 2013 at 10:56 PM (Answer #1)

dislike 1 like

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.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes