Numbers are the same
cos 1 > cos 1 ∘ cos 2 > cos 2 ∘ sin 1 > sin 1 ∘ sin 2 > sin 2 ∘
State the above statements as True or False from the top down to the bottom. T is for True and F is for False statement.
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2 solutions
Moderator note:
Correct! Although it would be better to clarify this line
Now for statement 4, 2 radian is closer to pi/2 than pi
Actually which one is radiant? In my country we are using pi for radiant.
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If there is a circle sign: ∘ as a superscript of the number, then it is in degrees, else it's a convention to treat it as radians.
In general, for x ∈ [ 0 , π ] ⇒ { cos x 1 < cos x 2 sin x 1 > sin x 2 if x 1 > x 2 if ∣ 2 π − x 1 ∣ < ∣ 2 π − x 2 ∣
Therefore, the answer is F F T T .
Moderator note:
Can you solve this question without using the fact that 1 radian is approximately 60 degrees?
As cosx is decreasing function between 0 and pi therefore statement 1 and statement 2 are false.
Also sinx is increasing function between 0 and pi/2 therefore statement 3 is true.
Now for statement 4, 2 radian is closer to pi/2 than pi therefore it has value close to 1 and sin 1 degree has value nearly 0 therefore statement 4 is true.