Examining a Curve - # 4

[Jason76]

First of all finding the critical numbers is a problem for this one:

\(\displaystyle f(x) = 3\sin(x) + 3\cos(x)\)

\(\displaystyle f'(x) = 3\cos(x) + [-3\sin(x)]\)

\(\displaystyle f'(x) = 3\cos(x) - 3\sin(x)\) Next move, hint?

 

[Deleted member 4993]

First of all finding the critical numbers is a problem for this one:

\(\displaystyle f(x) = 3\sin(x) + 3\cos(x)\)

\(\displaystyle f'(x) = 3\cos(x) + [-3\sin(x)]\)

\(\displaystyle f'(x) = 3\cos(x) - 3\sin(x)\) Next move, hint?

for critical number,

f'(x) = 0 [since the domain of sin(x) and cos(x) is (-\(\displaystyle \infty , +\infty \))]

f'(x) = 0 → sin(x) = cos(x) ............ now continue....

 

[Jason76]

Tough one. Have to ask the professor on this one.

 

[stapel]

Tough one. Have to ask the professor on this one.

Not really; you just needed to have taken pre-calculus before you enrolled for calculus, especially since this calculus course is obviously trig-based. The solution to this trig equation is actually quite simple.

 

[Deleted member 4993]

Tough one. Have to ask the professor on this one.

Use

\(\displaystyle cos(x) \ = \ sin\left(\dfrac{2n+1}{2}\pi - x \right )\)

 

[HallsofIvy]

Do you not see that sin(x)= cos(x) is the same as tan(x)= 1?

Or- since cos(t) is the x coordinate and sin(y) is the y coordinate of a point on the unit circle, this is the same as the line y= x crossing the unit circle.