A community for students.
Here's the question you clicked on:
 0 viewing
MathCurious
 2 years ago
sin (0.77x) = 1/2
How did they get 0.77x = 3.665 and 5.760?
Someone please help show me the steps of their work so I can see it.
MathCurious
 2 years ago
sin (0.77x) = 1/2 How did they get 0.77x = 3.665 and 5.760? Someone please help show me the steps of their work so I can see it.

This Question is Closed

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1I think there are two ways. The first is memorizing what you take the sine of to get 1/2. The other ways is using the inverse sine function. Because\[sin(77x)=\frac{1}{2}\], you can say \[77x = sin^{1}(\frac{1}{2})\]

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1This only helps if you have a calculator..

MathCurious
 2 years ago
Best ResponseYou've already chosen the best response.1Hello, thank you for answering. This is what I initially thought as well. however, the inverse sine of negative one half gave me: 0.5235987756 radians. Above it shows different answers for the solution.

MathCurious
 2 years ago
Best ResponseYou've already chosen the best response.1So I am baffled how my text came up with such a number.

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Huh! I'm foggy on trigonometry, sorry!

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1I used wolfram alpha to solve for \[a\]in\[sin(a)=\frac{1}{2}\] and it produced \[x=\frac{7\pi}{6}+2\pi n_1\]and\[x=\frac{11\pi}{6}+2\pi n_2\]

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1The first is 3.6651914291880921115397506138260866982300309659376234...

MathCurious
 2 years ago
Best ResponseYou've already chosen the best response.1Oh I see.. The 3.665 and 5.760 are just decimal equivalents of the fraction. Thanks for shedding some light on it.

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1If you got it, then congratulations! I'm still a bit confused! :)

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1The second resolves to 5.7595865315812876038481795360124219543614772321876940... when \[n_2=0\]

MathCurious
 2 years ago
Best ResponseYou've already chosen the best response.1Haha. I got it. It is saying. The sine function is equal to 1/2 in two different quadrants. In a circle (degrees) it is located at 7pi/6 and 11pi/6 These are equivalent to a 30 degree angle (pi/6) in the first quadrant. 7pi/6 = 3.665

MathCurious
 2 years ago
Best ResponseYou've already chosen the best response.1Excuse me, those are radians!

MathCurious
 2 years ago
Best ResponseYou've already chosen the best response.1Well thanks for guiding me. I got it. Medaled.

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Cool! Would you just have to memorize \[\frac{7\pi}{6}\] and \[\frac{11\pi}{6}\]? I think you would have to...

theEric
 2 years ago
Best ResponseYou've already chosen the best response.1Ah well, I'll recap another day! I'm glad I could be of some service! Take care!

MathCurious
 2 years ago
Best ResponseYou've already chosen the best response.1I wouldn't really memorize, but it's not a bad idea if you have that capacity! :) If anything it would be convenient. However, there is a method to finding it with logic. If the Ycoordinate is 1/2 then the x must be \[\sqrt{3}\div2\] this is assuming we understand the basic triangles. This information tells us with an xcoord of 1/2 and a ycoord of \[\sqrt{3}\div2\] it is a 30 degree angle (in quadrant I). However the problem needs a solution for where Y is negative. dw:1350355894146:dw It is true in two quadrants. The formula for DEGREES to RADIANS is:( DEGREE*PI )/ 180 since quadrant III begins from 180 and ends at 270 AND we knew it is essentially a 30 degree angle then we can add 30 DEGREES to 180. This becomes a 210 angle. Divide 270 by 180 and you get 7/6. Don't forget to multiply it by Pi. Hopefully that shows how to get an angle in another quadrant. There are of course other tricks to get there. dw:1350356151031:dw You could see this visually. You could just directly reflect the angle into an opposite quadrant by making a straight line out of it. Here it has 180 degrees added to it. So you don't need to just simply memorize radians.
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.