Docetaxel and Prednisone With or Without Cediranib in Treating Patients With Metastatic Prostate Cancer That Did Not Respond to Hormone Therapy

Inclusion Criteria: * Clinical/radiologic metastases with objective evidence of disease progression by imaging or by rising prostate-specific antigen (PSA) despite androgen deprivation therapy * Rising PSA must be determined based on a rising trend with 2 successive elevations at a minimum interval of 1 week * Meets 1 of the following criteria: Measurable disease, with any level of PSA, at least 1 unidimensionally measurable lesion (longest diameter to be recorded) \>= 20 mm by conventional techniques or \>= 10 mm by spiral CT scan, nonmeasurable disease, PSA \>= 5 ng/mL OR new areas of bony metastases on bone scan * Castrate levels of testosterone \< 50 ng/dL must be maintained and documented * Luteinizing hormone-releasing hormone (LHRH) agonist therapy must be continued, if required to maintain castrate levels of testosterone * Total bilirubin normal * Patients with radiological evidence of stable brain metastases are eligible provided they are asymptomatic and do not require corticosteroids or have been treated with corticosteroids and show clinical and radiological evidence of stabilization at least 10 days after discontinuation of steroids * ECOG performance status (PS) =\< 2 or Karnofsky PS 60-100% * Life expectancy \> 12 weeks * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelet count \>= 100,000/mcL * Histologically confirmed adenocarcinoma of the prostate * AST and ALT =\< 2.5 times upper limit of normal * Creatinine normal OR creatinine clearance \>= 60 mL/min * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * Proteinuria =\< 1+ and urine protein:creatinine ratio =\< 1.0 OR 24-hour urine protein \< 1,000 mg * Peripheral neuropathy \>= grade 2 * Uncontrolled intercurrent illness including, but not limited to, any of the following: ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, psychiatric illness/social situations that would limit compliance with study requirements * Congestive heart failure, second or third degree heart block, or recent myocardial infarction within the past 6 months * QTc prolongation \> 500 msec OR other ECG abnormality noted within 14 days of treatment * New York Heart Association class III or IV cardiac disease; Class II disease controlled with treatment and monitoring allowed * History of poorly controlled hypertension (e.g., resting blood pressure \> 150/90 mm Hg with or without hypertensive therapy) * History of a curatively treated malignancy with a survival prognosis of less than 5 years or concurrent malignancy except for adequately treated basal cell or squamous cell skin cancer or carcinoma in situ * History of significant gastrointestinal impairment, as judged by the investigator, that would significantly affect the absorption of cediranib * History of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80 * Significant hemorrhage (30 mL bleeding/episode in previous 3 months) or hemoptysis (5 mL fresh blood in previous 4 weeks) * Prior enrollment or randomization of treatment in the present study * Patients must be off flutamide antiandrogen therapy for ≥ 4 weeks (6 weeks for bicalutamide or nilutamide) * No prior chemotherapy for metastatic prostate cancer * No major surgery within the past 14 days or a surgical incision that is not fully healed * No HIV-positive patients on combination antiretroviral therapy * No conditions requiring concurrent use of drugs or biologics with proarrhythmic potential * No other investigational agents within 30 days prior to study enrollment * No untreated unstable brain or meningeal metastases * Known hypersensitivity to cediranib or any of its excipients