OPINION
W. FLETCHER, Circuit Judge:
Defendant Mariano Anguiano-Morfin appeals the district court’s denial of his motion for a new trial. Anguiano, a former lawful permanent resident of the United States, was removed to Mexico in early 2010. After his removal, Anguiano approached a United States port of entry and told the border agent that he was a U.S. citizen. He was arrested and tried under 18 U.S.C. § 911 for making a false claim of citizenship. His sole defense at trial was that he suffered from a delusion that caused him genuinely to believe that he was a United States citizen. Anguiano argued that his misstatement was therefore not willful as required by the statute. The jury convicted Anguiano, and the district court denied his motion for a new trial. We have jurisdiction under 28 U.S.C. § 1291 and we affirm.
I. Jury Instructions
Anguiano’s first argument is that the jury instructions were inadequate. “A criminal defendant has a constitutional right to have the jury instructed according to his theory of the case, provided that the requested instruction is supported by law and has some foundation in the evidence.” United States v. Marguet-Pillado, 648 F.3d 1001, 1006 (9th Cir.2011) (citations and internal quotation marks omitted). We review de novo whether an instruction is “supported by law.” Id. (internal quotation marks omitted). We review for an abuse of discretion whether it has “some foundation in the evidence.” Id. (internal quotation marks omitted). “The district court’s failure to give a defendant’s requested instruction that is supported by law and has some foundation in the evidence warrants per se reversal, unless other instructions, in their entirety, adequately cover that defense theory.” Id. (citations and internal quotation marks omitted). We review de novo whether other instructions adequately cover the defense theory. United States v. Mason, 902 F.2d 1434, 1438 (9th Cir.1990). We also review de novo whether the jury instructions correctly state the elements of a crime. United States v. Phillips, 367 F.3d 846, 854 (9th Cir.2004). “The district court has broad discretion in formulating the instructions” for both the elements and the theory of the defense, and it “need not give an instruction in the precise language proposed by the defendant.” United States v. Hayes, 794 F.2d 1348, 1351 (9th Cir.1986).
Anguiano was convicted under 18 U.S.C. § 911, which requires that a defendant “falsely and willfully represent ] himself to be a citizen of the United States.” The essential elements of a § 911 violation are that “(1) [the defendant] made a false claim of U.S. citizenship; (2) his misrepresentation was willful ...; and (3) it was conveyed to someone with good reason to inquire into his citizenship status.” United States v. Karaouni, 379 F.3d 1139, 1142 (9th Cir.2004).
Anguiano argues that the willfulness element of § 911 requires that the defendant know that his representation is false. We agree. Anguiano requested the following jury instruction, which the district court refused to give:
The defense has presented evidence that Mr. Anguiano Morfin genuinely, though mistakenly, believed he was a United States citizen when he claimed to be a United States citizen.
The Government must prove beyond a reasonable doubt that Mr. Anguiano Morfin knew that his claim to United States citizenship was false.
If, after considering the evidence, you are left with a reasonable doubt as to whether Mr. Anguiano Morfin knew his claim to United States citizenship was false, you must find Mr. Anguiano Mor-fin not guilty.
The second and third paragraphs of Angui-ano’s proposed instruction are an accurate statement of the law. Given Anguiano’s defense at trial, the best course would have been to include these paragraphs in the instructions.
We nonetheless conclude that the given instructions, considered as a whole, were adequate in the circumstances of this case. The instructions sufficiently conveyed the essential elements of the crime. See Hayes, 794 F.2d at 1351. The instructions stated that the “Government must prove ... beyond a reasonable doubt” that “the Defendant made such false representation willfully. That is, the misrepresentation was voluntarily and deliberately made.” Although Anguiano’s requested instruction more clearly articulated the knowledge requirement, the given instruction was adequate under the circumstances because a “misrepresentation ... deliberately made” suggests a knowing falsehood. Combined with the testimony and closing arguments at trial, which focused on what Anguiano knew, the jury was aware that his subjective belief was the dispositive issue. See United States v. Feingold, 454 F.3d 1001, 1012 (9th Cir.2006).
The instructions also adequately presented Anguiano’s theory of the case. The instructions stated that “[t]he theory of the defense is that the Defendant genuinely believes, though mistakenly, that he was a United States citizen when he claimed to be a United States citizen.” Coming in context after the legal definition of the essential elements, this instruction sufficiently conveyed the defense theory. See Marguet-Pillado, 648 F.3d at 1006.
II. Prosecutorial Misconduct
Anguiano’s second argument is that the prosecution improperly questioned his expert witness, Dr. Lavid. Anguiano did not object on this basis at trial, so we review for plain error. See Puckett v. United States, 556 U.S. 129, 135, 129 S.Ct. 1423, 173 L.Ed.2d 266 (2009). Anguiano has the burden to show that (1) there was an error; (2) the error was plain, i.e. clear or obvious; (3) the error affected his substantial rights, meaning that it “affected the outcome of the district court proceedings”; and (4) the error “seriously affects the fairness, integrity or public reputation of judicial proceedings.” Id. (alteration and internal quotation marks omitted).
Anguiano has not shown plain error. He argues that the prosecutor inappropriately asked Dr. Lavid to comment on Anguiano’s veracity. But given that Dr. Lavid had found Anguiano to be truthful as part of the basis for his diagnosis, questions on this subject were arguably proper. See In re Hanford Nuclear Reservation Litig., 534 F.3d 986, 1016 (9th Cir.2008) (“Opposing counsel may cross-examine an expert on the facts or data on which his opinion was based”). Any error here was not “plain” since it was not “clear or obvious under current law.” United States v. De La Fuente, 353 F.3d 766, 769 (9th Cir.2003). Anguiano also contends that the prosecutor improperly impugned Dr. Lavid’s trustworthiness and vouched for a government witness’s credibility. Even if true, Anguiano has failed to demonstrate that these remarks “affected the outcome” of the trial and “seriously affect[ed] the fairness, integrity or public reputation of judicial proceedings.” Puckett, 556 U.S. at 135,129 S.Ct. 1423.
AFFIRMED.