Separate $sin^-1 (cos theta + i sin theta)$ into real and imaginary parts [on hold]

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
1
down vote

favorite












I tried it but it became horribly long. Please suggest a concise method to solve it.






trigonometry







share|cite|improve this question















put on hold as off-topic by Did, Xander Henderson, hardmath, Micah, Key Flex 11 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, hardmath, Micah, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.












  • If you "tried it but it became horribly long", some details of how you approached this would make a welcome improvement. In its current form the body of the Question does not contain a problem statement, and it is not a good practice to rely solely on the title for the problem setup and goal. Please edit.
    – hardmath
    14 hours ago














up vote
1
down vote

favorite












I tried it but it became horribly long. Please suggest a concise method to solve it.






trigonometry







share|cite|improve this question















put on hold as off-topic by Did, Xander Henderson, hardmath, Micah, Key Flex 11 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, hardmath, Micah, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.












  • If you "tried it but it became horribly long", some details of how you approached this would make a welcome improvement. In its current form the body of the Question does not contain a problem statement, and it is not a good practice to rely solely on the title for the problem setup and goal. Please edit.
    – hardmath
    14 hours ago












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I tried it but it became horribly long. Please suggest a concise method to solve it.






trigonometry







share|cite|improve this question















I tried it but it became horribly long. Please suggest a concise method to solve it.






trigonometry




trigonometry






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 9 at 14:01









amWhy

190k27221433




190k27221433










asked Sep 9 at 13:44









Pratim Das

423




423




put on hold as off-topic by Did, Xander Henderson, hardmath, Micah, Key Flex 11 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, hardmath, Micah, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by Did, Xander Henderson, hardmath, Micah, Key Flex 11 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, hardmath, Micah, Key Flex
If this question can be reworded to fit the rules in the help center, please edit the question.











  • If you "tried it but it became horribly long", some details of how you approached this would make a welcome improvement. In its current form the body of the Question does not contain a problem statement, and it is not a good practice to rely solely on the title for the problem setup and goal. Please edit.
    – hardmath
    14 hours ago
















  • If you "tried it but it became horribly long", some details of how you approached this would make a welcome improvement. In its current form the body of the Question does not contain a problem statement, and it is not a good practice to rely solely on the title for the problem setup and goal. Please edit.
    – hardmath
    14 hours ago















If you "tried it but it became horribly long", some details of how you approached this would make a welcome improvement. In its current form the body of the Question does not contain a problem statement, and it is not a good practice to rely solely on the title for the problem setup and goal. Please edit.
– hardmath
14 hours ago




If you "tried it but it became horribly long", some details of how you approached this would make a welcome improvement. In its current form the body of the Question does not contain a problem statement, and it is not a good practice to rely solely on the title for the problem setup and goal. Please edit.
– hardmath
14 hours ago










1 Answer
1






active

oldest

votes

















up vote
2
down vote













Let $sin^-1(costheta+isintheta)$ be $a+bi$. Then



$costheta+isintheta=sin(a+bi)=sin acos (bi) + cos asin(bi)$



Now just express $cos(bi)$ and $sin(bi)$ in another way to get the real and imaginary parts.






share|cite|improve this answer



























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    2
    down vote













    Let $sin^-1(costheta+isintheta)$ be $a+bi$. Then



    $costheta+isintheta=sin(a+bi)=sin acos (bi) + cos asin(bi)$



    Now just express $cos(bi)$ and $sin(bi)$ in another way to get the real and imaginary parts.






    share|cite|improve this answer
























      up vote
      2
      down vote













      Let $sin^-1(costheta+isintheta)$ be $a+bi$. Then



      $costheta+isintheta=sin(a+bi)=sin acos (bi) + cos asin(bi)$



      Now just express $cos(bi)$ and $sin(bi)$ in another way to get the real and imaginary parts.






      share|cite|improve this answer






















        up vote
        2
        down vote










        up vote
        2
        down vote









        Let $sin^-1(costheta+isintheta)$ be $a+bi$. Then



        $costheta+isintheta=sin(a+bi)=sin acos (bi) + cos asin(bi)$



        Now just express $cos(bi)$ and $sin(bi)$ in another way to get the real and imaginary parts.






        share|cite|improve this answer












        Let $sin^-1(costheta+isintheta)$ be $a+bi$. Then



        $costheta+isintheta=sin(a+bi)=sin acos (bi) + cos asin(bi)$



        Now just express $cos(bi)$ and $sin(bi)$ in another way to get the real and imaginary parts.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Sep 9 at 13:53









        TonyK

        38.9k348127




        38.9k348127












            -

            這個網誌中的熱門文章

            How to combine Bézier curves to a surface?

            圖片
            Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of Bézier curves of different orders. But this algorithm is defined in a two dimensional space for now. To shift it into the third dimension I need to somehow combine the Bézier curves. Given two curves in each two dimensions, how can I combine them to build a surface? I thought about something like a curve of a curve. Or maybe I could multiply them somehow. How can I combine them to cause the wanted behavior? Is there a common approach? In the image you can see the input, on the left, and the output, on the right, of the algorithm that works in a two dimensional space. For the real application there is a three dimensional input. The algorithm relays only on the adjacent tiles. Given these it will define the control points of the mentioned Bézier curve. Additionally it marks one side of the curve as inside t
            閱讀完整內容

            Why am i infinitely getting the same tweet with the Twitter Search API?

            圖片
            up vote 0 down vote favorite My code workes perfectly for other queries, but for one query I am infinitely getting the same tweet. I can't understand what the problem is. API call: query='Allergic asthma OR Nonallergic asthma OR Occupational asthma OR EIB OR Exercise-induced bronchoconstriction OR Nocturnal asthma OR Cough-variant asthma' new_tweets = api.search(q=searchQuery, count=100, since_id=since_id, lang='en',tweet_mode='extended') if not new_tweets: print("No more tweets found") break for tweet in new_tweets: if True: print(jsonpickle.encode(tweet._json, unpicklable=False)) my_file = open('searchTweets.txt','a') my_file.write(jsonpickle.encode(tweet._json, unpicklable=False)+'n') my_file.close() else: continue Output in file: https://pastebin.com/JmRCsTeE These are the JSONs of the same Tweet. Other queries that work: Breast cancer OR Prostate cancer OR Colon cancer OR Lung cancer Type 2 dia
            閱讀完整內容

            Carbon dioxide

            圖片
            "CO2" redirects here. For other uses, see CO2 (disambiguation). Carbon dioxide Names Other names Carbonic acid gas Carbonic anhydride Carbonic oxide Carbon oxide Carbon(IV) oxide Dry ice (solid phase) Identifiers CAS Number 124-38-9   Y 3D model (JSmol) Interactive image Interactive image 3DMet B01131 Beilstein Reference 1900390 ChEBI CHEBI:16526   Y ChEMBL ChEMBL1231871   N ChemSpider 274   Y ECHA InfoCard 100.004.271 EC Number 204-696-9 E number E290 (preservatives) Gmelin Reference 989 KEGG D00004   Y MeSH Carbon+dioxide PubChem CID 280 RTECS number FF6400000 UNII 142M471B3J   Y UN number 1013 (gas), 1845 (solid) InChI InChI=1S/CO2/c2-1-3   Y Key: CURLTUGMZLYLDI-UHFFFAOYSA-N   Y InChI=1/CO2/c2-1-3 Key: CURLTUGMZLYLDI-UHFFFAOYAO SMILES O=C=O C(=O)=O Properties Chemical formula C O 2 Molar mass 44.01 g·mol −1 Appearance Colorless gas Odor Low concentrations: none High concentrations: sharp; acidic [1] Density 1562 kg/m 3 (solid at 1 atm and −78.5 °C) 1101 kg/m 3 (liquid at
            閱讀完整內容