Evaluate the limit of sin x + cos x, if x->pi/3?
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
To find the limit of sin x + cos x for x--> pi/3, we first substitute x with pi/3 to see if we get a valid solution.
sin x + cos x for x--> pi/3
=> sin (pi/3) + cos (pi/3)
we see that both sin (pi/3) and cos (pi/3) are defined.
sin (pi/3) = (sqrt 3) /2
cos ( pi/3) = 1/2
sin (pi/3) + cos (pi/3) = (sqrt 3 + 1)/2
Therefore the required limit is (sqrt 3 + 1)/2
Related Questions
- Prove the following identity: (1+ sin x + cos x) / (1+ sin x - cos x) = cot x/2
- 1 Educator Answer
- Prove that sin^4 x+cos^4 x+(sin^2 2x)/2=1
- 1 Educator Answer
- Prove the following identity: cos x + cos 2x + cos 3x = cos 2x(1 + 2cos x)
- 1 Educator Answer
- What are sin x, tan x, cot x, if 180<x<270 and cos x=-4/5?
- 1 Educator Answer
We'll evaluate the limit of the sum of the functions sine and cosine in this way;
limĀ (sin x + cos x) = lim sin x + lim cos x, x-> pi/3
We'll substitute x by the value of pi/3 and we'll get:
lim sin x + lim cos x = lim sin pi/3 + lim cos pi/3
sin pi/3 = sqrt3/2
cos pi/3 = 1/2
lim sin x + lim cos x = lim sqrt3/2 + lim 1/2
The limit of a constant function is the value of the constant:
lim sin x + lim cos x = sqrt3/2 + 1/2
limĀ (sin x + cos x) = (sqrt3 + 1)/2
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Student Answers