A Study of LY2189265 and Sitagliptin in Participants With Type 2 Diabetes

Inclusion Criteria: * are males or females, diagnosed with T2DM (Type 2 Diabetes Mellitus) for ≥3 months prior to screening * male participants with female partners of child-bearing potential, or partners who are pregnant or breastfeeding, agree to use a reliable method of contraception from the time of the first dose until 3 months after the last dose of investigational product, as determined by the investigator. The method may be one of the following: * condom with spermicidal agent * male participant sterilization * true abstinence (which is in line with the participant's usual lifestyle choice; withdrawal or calendar methods are not considered acceptable) * female participants not of child-bearing potential (that is, are postmenopausal or permanently sterilized \[such as, tubal occlusion, hysterectomy, bilateral salpingectomy\]). Such participants will not be required to use contraception but must test negative for pregnancy at the time of enrollment. Postmenopausal is defined as at least 1 year post cessation of menses (without an alternative medical cause) or at least 1 year of spontaneous amenorrhea, with follicle stimulating hormone (FSH) ≥40 milli-international units/milliliter (mIU/mL) * female participants who have undergone sterilization by tubal ligation: agree to use a condom in conjunction with spermicidal gel, foam, cream, film or suppository from the time of screening until 3 months after the last dose of investigational product. Such participants must also test negative for pregnancy at the time of enrollment * have a body mass index (BMI) of between 23.0 and 40.0 kilograms/meter squared (kg/m\^2), inclusive, at the time of screening * have T2DM controlled with diet and exercise alone, or are on a stable dose of metformin Immediate Release (IR) for at least 4 weeks prior to screening, or are on metformin Extended Release (ER) and are capable/willing to be switched onto metformin IR or washed out prior to the first dose of investigational product, or are on sulfonylureas, acarbose (or other disaccharidase inhibitors), thiazolidinediones, or meglitinides and are capable/willing to be washed out prior to the first dose of investigational product * have a fasting blood glucose value at screening ≤15.3 millimoles/liter (mmol/L) (275 milligrams/deciliter \[mg/dL\]) * have a glycosylated hemoglobin A1c (HbA1c) value at screening (or within 4 weeks prior to screening) of 6.5% to 10% * have clinical laboratory test results within normal reference range for the population or within normal reference range for the investigator site, or results with acceptable deviations that are judged to be not clinically significant by the investigator. Abnormalities of serum glucose, serum lipids, urinary glucose, and urinary protein consistent with T2DM are acceptable. * have creatinine clearance (CrCl) of greater than 50 milliliters/minute (mL/min) at screening estimated by the Cockcroft-Gault formula * have venous access sufficient to allow for blood sampling as per the protocol * are reliable and willing to make themselves available for the duration of the study and are willing to follow study procedures Exclusion Criteria: * are currently enrolled in, have completed or discontinued within the last 30 days from, a clinical trial involving an investigational product, or are concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study * have known allergies to glucagon-like-peptide 1 (GLP-1)-related compounds, including LY2189265 or to sitagliptin-related compounds or any components of either formulation * are persons who have previously completed or withdrawn from this study or any other study investigating LY2189265 in the 3 months prior to screening or have received glucagon-like peptides or incretin mimetics in the 3 months prior to screening * have taken insulin, chlorpropamide, or alpha-glucosidase inhibitors within 30 days prior to screening * have an abnormality in the 12-lead electrocardiogram (ECG) that, in the opinion of the investigator, increases the risks associated with participating in the study * have poorly controlled hypertension (systolic blood pressure \[BP\] \>160 millimeters of mercury \[mmHg\] and/or diastolic BP \>100 mmHg) and/or evidence of labile BP including symptomatic postural hypotension * have a history or presence of respiratory, hepatic, renal, endocrine, hematological, or neurological disorders capable of significantly altering the absorption, metabolism, or elimination of drugs; of constituting a risk when taking the study medication; or of interfering with the interpretation of data * have a history or presence of cardiovascular disorder (including myocardial infarction, cerebrovascular accident, venous thromboembolism, arrhythmia \[judged by the investigator to be clinically significant\], or angina) within the last year, have symptoms or signs of congestive heart failure, or are expected to require coronary artery bypass surgery or angioplasty * have a history or presence of pancreatitis (history of chronic pancreatitis or idiopathic acute pancreatitis) or gastrointestinal disorder, for example relevant esophageal reflux or gall bladder disease, or any gastrointestinal disease which impacts gastric emptying (GE) (such as, gastric bypass surgery, pyloric stenosis, with the exception of appendectomy) or could be aggravated by GLP-1 analogs or dipeptidyl peptidase-4 (DPP-4) inhibitors. Participants with dyslipidemia, and participants who had cholecystolithiasis (removal of gall stones) and/or cholecystectomy (removal of gall bladder) in the past, with no further sequelae, may be included in the study at the discretion of the screening physician * have any existing medical condition that might interfere with interpretation of the data, including a history of gastrointestinal surgery (with the exception of appendectomy performed more than 12 months ago), peptic ulceration, gastrointestinal bleeding, diabetic gastroparesis, ulcerative colitis, Crohn's disease, Irritable Bowel Syndrome (IBS), gastric bypass, or laparoscopic gastric banding * show evidence of significant active neuropsychiatric disease * have had 2 or more episodes of severe hypoglycemia within the last 6 months prior to screening * have personal or family history of medullary thyroid cancer (MTC) or a genetic condition that predisposes to MTC * regularly uses known drugs of abuse and/or show positive findings on urinary drug screening * intend to start new concomitant medication during the study, including over-the-counter and herbal medication, regularly use drugs that directly reduce gastrointestinal motility and/or regularly use systemic corticosteroids by oral, intravenous, or intramuscular route, or potent, inhaled, or intranasal steroids known to have a high rate of systemic absorption * show evidence of human immunodeficiency virus (HIV) infection and/or positive human HIV antibodies * show evidence of hepatitis C and/or positive hepatitis C antibody * show evidence of hepatitis B and/or positive hepatitis B surface antigen * have donated blood of more than 500 milliliters (mL) within the last month prior to screening * have an average weekly alcohol intake that exceeds 21 units per week (males up to age 65) and 14 units per week (males over 65 and females), or are unwilling to stop alcohol consumption from Day -3 of each period until after the last pharmacokinetic (PK) sample has been taken for that period, or to limit alcohol intake to a maximum of 2 units/day on all other days from screening through to follow-up. (1 unit = 12 ounces \[oz\] or 360 mL of beer; 5 oz or 150 mL of wine; 1.5 oz or 45 mL of distilled spirits) * smoke more than 10 cigarettes (or equivalent in nicotine) per day, and are unwilling to refrain from smoking on the day of LY2189265/sitagliptin administration or are unable to abide by Clinical Research Unit (CRU) restrictions on other inpatient days * are participants who, in the opinion of the investigator, are in any way unsuitable to participate in the study * have any medical conditions, medical history or are taking any medication which are contraindicated