If y=sin(x-sinx), what is the smallest positive value of x for which the tangent line is parallel to the x-axis

(a) 1.677

(b) 2.310

(c) 3.142

(d) 3.973

(e) 6.283

Option b ) 2.310

Step-by-step explanation:

Given that the function is

For finding when the tangent is parallel to x axis, we must find the least positive value of x for which y' i.e. derivative =0

Differentiate y with respect to x using chain rule.

Equate this to 0

Either one factor should be zero.

x=2.31 satisfies this

For the other root,

Since positive least value is asked we can say

x =2.310

Option b

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answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)