Answer:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.
Step-by-step explanation:
In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.
Let u = 1 + sin(x).
This means du/dx = cos(x). This implies dx = du/cos(x).
Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.
∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))
= ∫(u^(-1/2) * du). Integrating:
(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.
Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!
Answer:
AC ≈ 10.3
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan48° = 
= 
= 
( multiply both sides by 9.3 )
9.3 × tan48° = AC , then
AC ≈ 10.3 ( to 3 sf )
Answer:
Step-by-step explanation:
Given [Missing from the question]
Equation:
Interval:
Required
Determine the values of 
The given expression:
... shows that the value of is positive
The cosine of an angle has positive values in the first and the fourth quadrants.
So, we have:
Take arccos of both sides
--- In the first quadrant
In the fourth quadrant, the value is:
So, the values of in degrees are:
Convert to radians (Multiply both angles by 
)
So, we have:
