Find its area. y = sec^2(x), y = 8 cos(x), −π/3 ≤ x ≤ π/3

Answer 1

Notice that at the intersection of the two curves, x = π/3
and we have symmetry, so we can take the area from 0 to π/3, then double

area = 2∫ (8cosx - sec^2 x) dx from 0 to π/3
= 2[8sinx - tanx] from 0 to π/3
= 2(8sin π/3 - tan π/3 - (8sin 0 - tan 0 )
= ......

your turn

Answer 2

Let me know what you get, they probably want an "exact" answer.

Answer 3

For sinπ/3, I got 16√(3)/2 but for tanπ/3, I don't know how to find the answer for it. I know at tanπ/3, sin=3/√(2) and cos= 1/√(2). Should that give me √(3)/2? So I got 16√(3)/2 -2√(3)/√(2) is the wrong answer

Answer 4

tan π/3 = √3
tan π/6 = 1/√3
One of those "standard" values.
learn it, love it.

Answer 5

like pi/3 = 60 degrees and pi/6 = 30 degrees :)