A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Evaluate the expression using an appropriate double angle formula.
cos^2(15)  sin^2(15)
anonymous
 4 years ago
Evaluate the expression using an appropriate double angle formula. cos^2(15)  sin^2(15)

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0cos^2(15)  sin^2(15) = cos 2*15 = cos 30 = (sqrt3)/2

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0use of the identtiy cos 2x = cos^2x  sin^2x

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0How? could you please explain in detail please?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0there is an established formula: cos 2x = cos^2x  sin^2x which is true for all angles x the reverse is also true: cos^2x  sin^2x = cos2x so if you substitute x = 15 you get cos^2(15)  sin^2(15) = cos(2*15) cos(2*15) = cos 30 now you can use a calculator to find the cosine of 30 you get 0.866 which is a valid answer  i used a special right angled triangle

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327846869523:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh got it ! thanks ! and how about this one, sin(105)cos(105) ? do i use sin2x = 2sinxcosx ? but how do i use that one ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yes sin 2x = 2 sinx cosx so sinx cos x =sin 2x/ 2 =( sin 210) / 2 to find sin 210 look up sin 210180 = 30 on your calculator this gives 0.5 now 210 degrees is in third quadrant where sine is negative so sin 210 = 0.5 so sin(105)cos(105) = sin 210 /2 = 0.5 / 2 = 0.25

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0could you check if this is correct, i just did it. 2sin(pi/8)cos(pi/8) 2sinx cosx = sin2x 2sin(pi/8) cos(pi/8)= sin2(pi/8) sin2(pi/8) = sin (1/4 pi) = 0.0137 is it correct ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0sinx cos x =sin 2x/ 2 =( sin 210) / 2 in this part, why did you divide it by 2 ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.02sinscosx = sin2x divide both sides by 2 sinx cos x = sin2x / 2 your original expression was sin(105)cos(105)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thanks a lot ! and the question i just did by myself, is it correct ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0correct up to last line sin pi/4  0.707 did you set the calculator to radians?  it might have been in degrees

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah  i just checked  you must have set it ti degrees to get .0137

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh i didnt change it to radians. i just changed it to radians, my answer is 0.7071

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0could you help me out with this question ? 6tan(75) / 1tan^2 (75)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0sorry  i would if i had time  gotta go out

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh alright, thanks a lot for your help !
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.