3. Find the area of the shaded region.
2 answers:
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We know that and
Substitute in the value.
Use a calculator to multiply.
Since and
, we can rewrite the right side of the equation as
Using the identity , we can subtract
from either side to obtain the identity
substituting that into our previous expression, the right side of our equation simply becomes
We can now write our whole equation as
Adding 2 to both sides:
dividing both sides by 3:
When 0 ≤ x ≤ π, tan x can only be equal to 1 when sin x = cos x, which happens at x = π/4, and it can only be equal to -1 when -sin x = cos x, which happens at x = 3π/4