Question

State the signs of cos 4radian and cos 4 degree. which of these two function is greater...

Answer 1

Answer:

Cos 4° > Cos 4 radian

Step-by-step explanation:

State the signs of cos 4radian and cos 4 degree. which of these two function is greater...

Cos 4 radian =   4 * 180 /3.14 deg = 229.3 deg

=> 4 radian lies in 3rs Quadrant

=> Sign is -ve

cos 4 degree lies in 1st quadrant so sign is + ve

Cos 4° > Cos 4 radian

Answer 2

we know, relation between radian and degree .ie., π rad = 180°

or, 1 rad = (180/π)°

or, 4 rad = [(180/π) × 4]°

but π = 22/7

so, 4 rad = [(180 × 7/22) × 4]°

= (180 × 7 × 4/22)°

≈ 229.09°

now, cos(4 rad) = cos(229.09°)

we know, cos(180° + x ) = -cosx

so, cos(229.09°) = cos(180° + 49.09°)

= -cos(49.09°) ⇒negative value

[ note : cosine value is positive between 0 to 90° , so cos(49.09°) is positive and then, -cos(49.09°) will be negative ]

now, cos(4°) ⇒positive value

now, we have to find out greater value of cosine .

here I want to mention an important concept,

if cosx > cosy then, x < y , where x , y $\in$ (0, π/2)

[this is because cosine function is decreasing function between 0 to π/2. ]

here, 49.09° > 4°

then, cos(49.09°) < cos4°

or, |-cos(49.09°)| < cos4°

or, |cos(180° + 49.09°)| < cos4°

or, |cos(229.09°)| < cos4°

or, |cos(4 rad)| < cos4°

[ here I mentioned modulus of cos(4rad) , because actual value of cos(4rad) is negative but we have to compare absolute value of them. ]